category_theory.limits.preserves.opposites
⟷
Mathlib.CategoryTheory.Limits.Preserves.Opposites
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(last sync)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -64,7 +64,7 @@ def preservesLimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesColim
def preservesLimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesColimit K.op F] :
PreservesLimit K F.rightOp
where preserves c hc :=
- isLimitConeRightOpOfCocone _ (isColimitOfPreserves F (isColimitConeOp _ hc))
+ isLimitConeRightOpOfCocone _ (isColimitOfPreserves F (CategoryTheory.Limits.IsLimit.op _ hc))
#align category_theory.limits.preserves_limit_right_op CategoryTheory.Limits.preservesLimitRightOp
-/
@@ -74,7 +74,7 @@ def preservesLimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesColimit K.
def preservesLimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimit K.op F] :
PreservesLimit K F.unop
where preserves c hc :=
- isLimitConeUnopOfCocone _ (isColimitOfPreserves F (isColimitConeOp _ hc))
+ isLimitConeUnopOfCocone _ (isColimitOfPreserves F (CategoryTheory.Limits.IsLimit.op _ hc))
#align category_theory.limits.preserves_limit_unop CategoryTheory.Limits.preservesLimitUnop
-/
@@ -104,7 +104,7 @@ def preservesColimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesLim
def preservesColimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesLimit K.op F] :
PreservesColimit K F.rightOp
where preserves c hc :=
- isColimitCoconeRightOpOfCone _ (isLimitOfPreserves F (isLimitCoconeOp _ hc))
+ isColimitCoconeRightOpOfCone _ (isLimitOfPreserves F (CategoryTheory.Limits.IsColimit.op _ hc))
#align category_theory.limits.preserves_colimit_right_op CategoryTheory.Limits.preservesColimitRightOp
-/
@@ -114,7 +114,7 @@ def preservesColimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesLimit K.
def preservesColimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimit K.op F] :
PreservesColimit K F.unop
where preserves c hc :=
- isColimitCoconeUnopOfCone _ (isLimitOfPreserves F (isLimitCoconeOp _ hc))
+ isColimitCoconeUnopOfCone _ (isLimitOfPreserves F (CategoryTheory.Limits.IsColimit.op _ hc))
#align category_theory.limits.preserves_colimit_unop CategoryTheory.Limits.preservesColimitUnop
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
-import Mathbin.CategoryTheory.Limits.Opposites
-import Mathbin.CategoryTheory.Limits.Preserves.Finite
+import CategoryTheory.Limits.Opposites
+import CategoryTheory.Limits.Preserves.Finite
#align_import category_theory.limits.preserves.opposites from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.limits.preserves.opposites
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Limits.Opposites
import Mathbin.CategoryTheory.Limits.Preserves.Finite
+#align_import category_theory.limits.preserves.opposites from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
/-!
# Limit preservation properties of `functor.op` and related constructions
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
! This file was ported from Lean 3 source module category_theory.limits.preserves.opposites
-! leanprover-community/mathlib commit 9ed4366659f4fcca0ee70310d26ac5518dcb6dd0
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.Limits.Preserves.Finite
/-!
# Limit preservation properties of `functor.op` and related constructions
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
We formulate conditions about `F` which imply that `F.op`, `F.unop`, `F.left_op` and `F.right_op`
preserve certain (co)limits.
mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931
@@ -39,13 +39,16 @@ variable {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₂} D]
variable {J : Type w} [Category.{w'} J]
+#print CategoryTheory.Limits.preservesLimitOp /-
/-- If `F : C ⥤ D` preserves colimits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves
limits of `K : J ⥤ Cᵒᵖ`. -/
def preservesLimitOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ D) [PreservesColimit K.leftOp F] : PreservesLimit K F.op
where preserves c hc :=
isLimitConeRightOpOfCocone _ (isColimitOfPreserves F (isColimitCoconeLeftOpOfCone _ hc))
#align category_theory.limits.preserves_limit_op CategoryTheory.Limits.preservesLimitOp
+-/
+#print CategoryTheory.Limits.preservesLimitLeftOp /-
/-- If `F : C ⥤ Dᵒᵖ` preserves colimits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.left_op : Cᵒᵖ ⥤ D`
preserves limits of `K : J ⥤ Cᵒᵖ`. -/
def preservesLimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesColimit K.leftOp F] :
@@ -53,7 +56,9 @@ def preservesLimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesColim
where preserves c hc :=
isLimitConeUnopOfCocone _ (isColimitOfPreserves F (isColimitCoconeLeftOpOfCone _ hc))
#align category_theory.limits.preserves_limit_left_op CategoryTheory.Limits.preservesLimitLeftOp
+-/
+#print CategoryTheory.Limits.preservesLimitRightOp /-
/-- If `F : Cᵒᵖ ⥤ D` preserves colimits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.right_op : C ⥤ Dᵒᵖ` preserves
limits of `K : J ⥤ C`. -/
def preservesLimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesColimit K.op F] :
@@ -61,7 +66,9 @@ def preservesLimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesColimit K.
where preserves c hc :=
isLimitConeRightOpOfCocone _ (isColimitOfPreserves F (isColimitConeOp _ hc))
#align category_theory.limits.preserves_limit_right_op CategoryTheory.Limits.preservesLimitRightOp
+-/
+#print CategoryTheory.Limits.preservesLimitUnop /-
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.unop : C ⥤ D` preserves
limits of `K : J ⥤ C`. -/
def preservesLimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimit K.op F] :
@@ -69,7 +76,9 @@ def preservesLimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimit
where preserves c hc :=
isLimitConeUnopOfCocone _ (isColimitOfPreserves F (isColimitConeOp _ hc))
#align category_theory.limits.preserves_limit_unop CategoryTheory.Limits.preservesLimitUnop
+-/
+#print CategoryTheory.Limits.preservesColimitOp /-
/-- If `F : C ⥤ D` preserves limits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves
colimits of `K : J ⥤ Cᵒᵖ`. -/
def preservesColimitOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ D) [PreservesLimit K.leftOp F] :
@@ -77,7 +86,9 @@ def preservesColimitOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ D) [PreservesLimit K.leftO
where preserves c hc :=
isColimitCoconeRightOpOfCone _ (isLimitOfPreserves F (isLimitConeLeftOpOfCocone _ hc))
#align category_theory.limits.preserves_colimit_op CategoryTheory.Limits.preservesColimitOp
+-/
+#print CategoryTheory.Limits.preservesColimitLeftOp /-
/-- If `F : C ⥤ Dᵒᵖ` preserves limits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.left_op : Cᵒᵖ ⥤ D` preserves
colimits of `K : J ⥤ Cᵒᵖ`. -/
def preservesColimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesLimit K.leftOp F] :
@@ -85,7 +96,9 @@ def preservesColimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesLim
where preserves c hc :=
isColimitCoconeUnopOfCone _ (isLimitOfPreserves F (isLimitConeLeftOpOfCocone _ hc))
#align category_theory.limits.preserves_colimit_left_op CategoryTheory.Limits.preservesColimitLeftOp
+-/
+#print CategoryTheory.Limits.preservesColimitRightOp /-
/-- If `F : Cᵒᵖ ⥤ D` preserves limits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.right_op : C ⥤ Dᵒᵖ` preserves
colimits of `K : J ⥤ C`. -/
def preservesColimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesLimit K.op F] :
@@ -93,7 +106,9 @@ def preservesColimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesLimit K.
where preserves c hc :=
isColimitCoconeRightOpOfCone _ (isLimitOfPreserves F (isLimitCoconeOp _ hc))
#align category_theory.limits.preserves_colimit_right_op CategoryTheory.Limits.preservesColimitRightOp
+-/
+#print CategoryTheory.Limits.preservesColimitUnop /-
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.unop : C ⥤ D` preserves
colimits of `K : J ⥤ C`. -/
def preservesColimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimit K.op F] :
@@ -101,100 +116,133 @@ def preservesColimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimit
where preserves c hc :=
isColimitCoconeUnopOfCone _ (isLimitOfPreserves F (isLimitCoconeOp _ hc))
#align category_theory.limits.preserves_colimit_unop CategoryTheory.Limits.preservesColimitUnop
+-/
section
variable (J)
+#print CategoryTheory.Limits.preservesLimitsOfShapeOp /-
/-- If `F : C ⥤ D` preserves colimits of shape `Jᵒᵖ`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits of
shape `J`. -/
def preservesLimitsOfShapeOp (F : C ⥤ D) [PreservesColimitsOfShape Jᵒᵖ F] :
PreservesLimitsOfShape J F.op where PreservesLimit K := preservesLimitOp K F
#align category_theory.limits.preserves_limits_of_shape_op CategoryTheory.Limits.preservesLimitsOfShapeOp
+-/
+#print CategoryTheory.Limits.preservesLimitsOfShapeLeftOp /-
/-- If `F : C ⥤ Dᵒᵖ` preserves colimits of shape `Jᵒᵖ`, then `F.left_op : Cᵒᵖ ⥤ D` preserves limits
of shape `J`. -/
def preservesLimitsOfShapeLeftOp (F : C ⥤ Dᵒᵖ) [PreservesColimitsOfShape Jᵒᵖ F] :
PreservesLimitsOfShape J F.leftOp where PreservesLimit K := preservesLimitLeftOp K F
#align category_theory.limits.preserves_limits_of_shape_left_op CategoryTheory.Limits.preservesLimitsOfShapeLeftOp
+-/
+#print CategoryTheory.Limits.preservesLimitsOfShapeRightOp /-
/-- If `F : Cᵒᵖ ⥤ D` preserves colimits of shape `Jᵒᵖ`, then `F.right_op : C ⥤ Dᵒᵖ` preserves limits
of shape `J`. -/
def preservesLimitsOfShapeRightOp (F : Cᵒᵖ ⥤ D) [PreservesColimitsOfShape Jᵒᵖ F] :
PreservesLimitsOfShape J F.rightOp where PreservesLimit K := preservesLimitRightOp K F
#align category_theory.limits.preserves_limits_of_shape_right_op CategoryTheory.Limits.preservesLimitsOfShapeRightOp
+-/
+#print CategoryTheory.Limits.preservesLimitsOfShapeUnop /-
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits of shape `Jᵒᵖ`, then `F.unop : C ⥤ D` preserves limits of
shape `J`. -/
def preservesLimitsOfShapeUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimitsOfShape Jᵒᵖ F] :
PreservesLimitsOfShape J F.unop where PreservesLimit K := preservesLimitUnop K F
#align category_theory.limits.preserves_limits_of_shape_unop CategoryTheory.Limits.preservesLimitsOfShapeUnop
+-/
+#print CategoryTheory.Limits.preservesColimitsOfShapeOp /-
/-- If `F : C ⥤ D` preserves limits of shape `Jᵒᵖ`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits of
shape `J`. -/
def preservesColimitsOfShapeOp (F : C ⥤ D) [PreservesLimitsOfShape Jᵒᵖ F] :
PreservesColimitsOfShape J F.op where PreservesColimit K := preservesColimitOp K F
#align category_theory.limits.preserves_colimits_of_shape_op CategoryTheory.Limits.preservesColimitsOfShapeOp
+-/
+#print CategoryTheory.Limits.preservesColimitsOfShapeLeftOp /-
/-- If `F : C ⥤ Dᵒᵖ` preserves limits of shape `Jᵒᵖ`, then `F.left_op : Cᵒᵖ ⥤ D` preserves colimits
of shape `J`. -/
def preservesColimitsOfShapeLeftOp (F : C ⥤ Dᵒᵖ) [PreservesLimitsOfShape Jᵒᵖ F] :
PreservesColimitsOfShape J F.leftOp where PreservesColimit K := preservesColimitLeftOp K F
#align category_theory.limits.preserves_colimits_of_shape_left_op CategoryTheory.Limits.preservesColimitsOfShapeLeftOp
+-/
+#print CategoryTheory.Limits.preservesColimitsOfShapeRightOp /-
/-- If `F : Cᵒᵖ ⥤ D` preserves limits of shape `Jᵒᵖ`, then `F.right_op : C ⥤ Dᵒᵖ` preserves colimits
of shape `J`. -/
def preservesColimitsOfShapeRightOp (F : Cᵒᵖ ⥤ D) [PreservesLimitsOfShape Jᵒᵖ F] :
PreservesColimitsOfShape J F.rightOp where PreservesColimit K := preservesColimitRightOp K F
#align category_theory.limits.preserves_colimits_of_shape_right_op CategoryTheory.Limits.preservesColimitsOfShapeRightOp
+-/
+#print CategoryTheory.Limits.preservesColimitsOfShapeUnop /-
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits of shape `Jᵒᵖ`, then `F.unop : C ⥤ D` preserves colimits
of shape `J`. -/
def preservesColimitsOfShapeUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimitsOfShape Jᵒᵖ F] :
PreservesColimitsOfShape J F.unop where PreservesColimit K := preservesColimitUnop K F
#align category_theory.limits.preserves_colimits_of_shape_unop CategoryTheory.Limits.preservesColimitsOfShapeUnop
+-/
end
+#print CategoryTheory.Limits.preservesLimitsOp /-
/-- If `F : C ⥤ D` preserves colimits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits. -/
def preservesLimitsOp (F : C ⥤ D) [PreservesColimits F] : PreservesLimits F.op
where PreservesLimitsOfShape J _ := preserves_limits_of_shape_op J F
#align category_theory.limits.preserves_limits_op CategoryTheory.Limits.preservesLimitsOp
+-/
+#print CategoryTheory.Limits.preservesLimitsLeftOp /-
/-- If `F : C ⥤ Dᵒᵖ` preserves colimits, then `F.left_op : Cᵒᵖ ⥤ D` preserves limits. -/
def preservesLimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesColimits F] : PreservesLimits F.leftOp
where PreservesLimitsOfShape J _ := preserves_limits_of_shape_left_op J F
#align category_theory.limits.preserves_limits_left_op CategoryTheory.Limits.preservesLimitsLeftOp
+-/
+#print CategoryTheory.Limits.preservesLimitsRightOp /-
/-- If `F : Cᵒᵖ ⥤ D` preserves colimits, then `F.right_op : C ⥤ Dᵒᵖ` preserves limits. -/
def preservesLimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesColimits F] : PreservesLimits F.rightOp
where PreservesLimitsOfShape J _ := preserves_limits_of_shape_right_op J F
#align category_theory.limits.preserves_limits_right_op CategoryTheory.Limits.preservesLimitsRightOp
+-/
+#print CategoryTheory.Limits.preservesLimitsUnop /-
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits, then `F.unop : C ⥤ D` preserves limits. -/
def preservesLimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimits F] : PreservesLimits F.unop
where PreservesLimitsOfShape J _ := preserves_limits_of_shape_unop J F
#align category_theory.limits.preserves_limits_unop CategoryTheory.Limits.preservesLimitsUnop
+-/
+#print CategoryTheory.Limits.perservesColimitsOp /-
/-- If `F : C ⥤ D` preserves limits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits. -/
def perservesColimitsOp (F : C ⥤ D) [PreservesLimits F] : PreservesColimits F.op
where PreservesColimitsOfShape J _ := preserves_colimits_of_shape_op J F
#align category_theory.limits.perserves_colimits_op CategoryTheory.Limits.perservesColimitsOp
+-/
+#print CategoryTheory.Limits.preservesColimitsLeftOp /-
/-- If `F : C ⥤ Dᵒᵖ` preserves limits, then `F.left_op : Cᵒᵖ ⥤ D` preserves colimits. -/
def preservesColimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesLimits F] : PreservesColimits F.leftOp
where PreservesColimitsOfShape J _ := preserves_colimits_of_shape_left_op J F
#align category_theory.limits.preserves_colimits_left_op CategoryTheory.Limits.preservesColimitsLeftOp
+-/
+#print CategoryTheory.Limits.preservesColimitsRightOp /-
/-- If `F : Cᵒᵖ ⥤ D` preserves limits, then `F.right_op : C ⥤ Dᵒᵖ` preserves colimits. -/
def preservesColimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesLimits F] : PreservesColimits F.rightOp
where PreservesColimitsOfShape J _ := preserves_colimits_of_shape_right_op J F
#align category_theory.limits.preserves_colimits_right_op CategoryTheory.Limits.preservesColimitsRightOp
+-/
+#print CategoryTheory.Limits.preservesColimitsUnop /-
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits, then `F.unop : C ⥤ D` preserves colimits. -/
def preservesColimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimits F] : PreservesColimits F.unop
where PreservesColimitsOfShape J _ := preserves_colimits_of_shape_unop J F
#align category_theory.limits.preserves_colimits_unop CategoryTheory.Limits.preservesColimitsUnop
+-/
end
@@ -204,59 +252,75 @@ section
-- universe.
variable {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₁} D]
+#print CategoryTheory.Limits.preservesFiniteLimitsOp /-
/-- If `F : C ⥤ D` preserves finite colimits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite
limits. -/
def preservesFiniteLimitsOp (F : C ⥤ D) [PreservesFiniteColimits F] : PreservesFiniteLimits F.op
where PreservesFiniteLimits J _ _ := preserves_limits_of_shape_op J F
#align category_theory.limits.preserves_finite_limits_op CategoryTheory.Limits.preservesFiniteLimitsOp
+-/
+#print CategoryTheory.Limits.preservesFiniteLimitsLeftOp /-
/-- If `F : C ⥤ Dᵒᵖ` preserves finite colimits, then `F.left_op : Cᵒᵖ ⥤ D` preserves finite
limits. -/
def preservesFiniteLimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesFiniteColimits F] :
PreservesFiniteLimits F.leftOp
where PreservesFiniteLimits J _ _ := preserves_limits_of_shape_left_op J F
#align category_theory.limits.preserves_finite_limits_left_op CategoryTheory.Limits.preservesFiniteLimitsLeftOp
+-/
+#print CategoryTheory.Limits.preservesFiniteLimitsRightOp /-
/-- If `F : Cᵒᵖ ⥤ D` preserves finite colimits, then `F.right_op : C ⥤ Dᵒᵖ` preserves finite
limits. -/
def preservesFiniteLimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesFiniteColimits F] :
PreservesFiniteLimits F.rightOp
where PreservesFiniteLimits J _ _ := preserves_limits_of_shape_right_op J F
#align category_theory.limits.preserves_finite_limits_right_op CategoryTheory.Limits.preservesFiniteLimitsRightOp
+-/
+#print CategoryTheory.Limits.preservesFiniteLimitsUnop /-
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite colimits, then `F.unop : C ⥤ D` preserves finite
limits. -/
def preservesFiniteLimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesFiniteColimits F] :
PreservesFiniteLimits F.unop
where PreservesFiniteLimits J _ _ := preserves_limits_of_shape_unop J F
#align category_theory.limits.preserves_finite_limits_unop CategoryTheory.Limits.preservesFiniteLimitsUnop
+-/
+#print CategoryTheory.Limits.preservesFiniteColimitsOp /-
/-- If `F : C ⥤ D` preserves finite limits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite
colimits. -/
def preservesFiniteColimitsOp (F : C ⥤ D) [PreservesFiniteLimits F] : PreservesFiniteColimits F.op
where PreservesFiniteColimits J _ _ := preserves_colimits_of_shape_op J F
#align category_theory.limits.preserves_finite_colimits_op CategoryTheory.Limits.preservesFiniteColimitsOp
+-/
+#print CategoryTheory.Limits.preservesFiniteColimitsLeftOp /-
/-- If `F : C ⥤ Dᵒᵖ` preserves finite limits, then `F.left_op : Cᵒᵖ ⥤ D` preserves finite
colimits. -/
def preservesFiniteColimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesFiniteLimits F] :
PreservesFiniteColimits F.leftOp
where PreservesFiniteColimits J _ _ := preserves_colimits_of_shape_left_op J F
#align category_theory.limits.preserves_finite_colimits_left_op CategoryTheory.Limits.preservesFiniteColimitsLeftOp
+-/
+#print CategoryTheory.Limits.preservesFiniteColimitsRightOp /-
/-- If `F : Cᵒᵖ ⥤ D` preserves finite limits, then `F.right_op : C ⥤ Dᵒᵖ` preserves finite
colimits. -/
def preservesFiniteColimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesFiniteLimits F] :
PreservesFiniteColimits F.rightOp
where PreservesFiniteColimits J _ _ := preserves_colimits_of_shape_right_op J F
#align category_theory.limits.preserves_finite_colimits_right_op CategoryTheory.Limits.preservesFiniteColimitsRightOp
+-/
+#print CategoryTheory.Limits.preservesFiniteColimitsUnop /-
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite limits, then `F.unop : C ⥤ D` preserves finite
colimits. -/
def preservesFiniteColimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesFiniteLimits F] :
PreservesFiniteColimits F.unop
where PreservesFiniteColimits J _ _ := preserves_colimits_of_shape_unop J F
#align category_theory.limits.preserves_finite_colimits_unop CategoryTheory.Limits.preservesFiniteColimitsUnop
+-/
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -56,7 +56,7 @@ def preservesLimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesColim
def preservesLimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesColimit K.op F] :
PreservesLimit K F.rightOp where
preserves {_} hc :=
- isLimitConeRightOpOfCocone _ (isColimitOfPreserves F (isColimitConeOp _ hc))
+ isLimitConeRightOpOfCocone _ (isColimitOfPreserves F hc.op)
#align category_theory.limits.preserves_limit_right_op CategoryTheory.Limits.preservesLimitRightOp
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.unop : C ⥤ D` preserves
@@ -64,7 +64,7 @@ def preservesLimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesColimit K.
def preservesLimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimit K.op F] :
PreservesLimit K F.unop where
preserves {_} hc :=
- isLimitConeUnopOfCocone _ (isColimitOfPreserves F (isColimitConeOp _ hc))
+ isLimitConeUnopOfCocone _ (isColimitOfPreserves F hc.op)
#align category_theory.limits.preserves_limit_unop CategoryTheory.Limits.preservesLimitUnop
/-- If `F : C ⥤ D` preserves limits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves
@@ -88,7 +88,7 @@ def preservesColimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesLim
def preservesColimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesLimit K.op F] :
PreservesColimit K F.rightOp where
preserves {_} hc :=
- isColimitCoconeRightOpOfCone _ (isLimitOfPreserves F (isLimitCoconeOp _ hc))
+ isColimitCoconeRightOpOfCone _ (isLimitOfPreserves F hc.op)
#align category_theory.limits.preserves_colimit_right_op CategoryTheory.Limits.preservesColimitRightOp
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.unop : C ⥤ D` preserves
@@ -96,7 +96,7 @@ def preservesColimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesLimit K.
def preservesColimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimit K.op F] :
PreservesColimit K F.unop where
preserves {_} hc :=
- isColimitCoconeUnopOfCone _ (isLimitOfPreserves F (isLimitCoconeOp _ hc))
+ isColimitCoconeUnopOfCone _ (isLimitOfPreserves F hc.op)
#align category_theory.limits.preserves_colimit_unop CategoryTheory.Limits.preservesColimitUnop
section
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -33,7 +33,6 @@ namespace CategoryTheory.Limits
section
variable {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₂} D]
-
variable {J : Type w} [Category.{w'} J]
/-- If `F : C ⥤ D` preserves colimits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves
@@ -38,64 +38,65 @@ variable {J : Type w} [Category.{w'} J]
/-- If `F : C ⥤ D` preserves colimits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves
limits of `K : J ⥤ Cᵒᵖ`. -/
-def preservesLimitOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ D) [PreservesColimit K.leftOp F] : PreservesLimit K F.op
- where preserves {_} hc :=
+def preservesLimitOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ D) [PreservesColimit K.leftOp F] :
+ PreservesLimit K F.op where
+ preserves {_} hc :=
isLimitConeRightOpOfCocone _ (isColimitOfPreserves F (isColimitCoconeLeftOpOfCone _ hc))
#align category_theory.limits.preserves_limit_op CategoryTheory.Limits.preservesLimitOp
/-- If `F : C ⥤ Dᵒᵖ` preserves colimits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.left_op : Cᵒᵖ ⥤ D`
preserves limits of `K : J ⥤ Cᵒᵖ`. -/
def preservesLimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesColimit K.leftOp F] :
- PreservesLimit K F.leftOp
- where preserves {_} hc :=
+ PreservesLimit K F.leftOp where
+ preserves {_} hc :=
isLimitConeUnopOfCocone _ (isColimitOfPreserves F (isColimitCoconeLeftOpOfCone _ hc))
#align category_theory.limits.preserves_limit_left_op CategoryTheory.Limits.preservesLimitLeftOp
/-- If `F : Cᵒᵖ ⥤ D` preserves colimits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.right_op : C ⥤ Dᵒᵖ` preserves
limits of `K : J ⥤ C`. -/
def preservesLimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesColimit K.op F] :
- PreservesLimit K F.rightOp
- where preserves {_} hc :=
+ PreservesLimit K F.rightOp where
+ preserves {_} hc :=
isLimitConeRightOpOfCocone _ (isColimitOfPreserves F (isColimitConeOp _ hc))
#align category_theory.limits.preserves_limit_right_op CategoryTheory.Limits.preservesLimitRightOp
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.unop : C ⥤ D` preserves
limits of `K : J ⥤ C`. -/
def preservesLimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimit K.op F] :
- PreservesLimit K F.unop
- where preserves {_} hc :=
+ PreservesLimit K F.unop where
+ preserves {_} hc :=
isLimitConeUnopOfCocone _ (isColimitOfPreserves F (isColimitConeOp _ hc))
#align category_theory.limits.preserves_limit_unop CategoryTheory.Limits.preservesLimitUnop
/-- If `F : C ⥤ D` preserves limits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves
colimits of `K : J ⥤ Cᵒᵖ`. -/
def preservesColimitOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ D) [PreservesLimit K.leftOp F] :
- PreservesColimit K F.op
- where preserves {_} hc :=
+ PreservesColimit K F.op where
+ preserves {_} hc :=
isColimitCoconeRightOpOfCone _ (isLimitOfPreserves F (isLimitConeLeftOpOfCocone _ hc))
#align category_theory.limits.preserves_colimit_op CategoryTheory.Limits.preservesColimitOp
/-- If `F : C ⥤ Dᵒᵖ` preserves limits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.left_op : Cᵒᵖ ⥤ D` preserves
colimits of `K : J ⥤ Cᵒᵖ`. -/
def preservesColimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesLimit K.leftOp F] :
- PreservesColimit K F.leftOp
- where preserves {_} hc :=
+ PreservesColimit K F.leftOp where
+ preserves {_} hc :=
isColimitCoconeUnopOfCone _ (isLimitOfPreserves F (isLimitConeLeftOpOfCocone _ hc))
#align category_theory.limits.preserves_colimit_left_op CategoryTheory.Limits.preservesColimitLeftOp
/-- If `F : Cᵒᵖ ⥤ D` preserves limits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.right_op : C ⥤ Dᵒᵖ` preserves
colimits of `K : J ⥤ C`. -/
def preservesColimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesLimit K.op F] :
- PreservesColimit K F.rightOp
- where preserves {_} hc :=
+ PreservesColimit K F.rightOp where
+ preserves {_} hc :=
isColimitCoconeRightOpOfCone _ (isLimitOfPreserves F (isLimitCoconeOp _ hc))
#align category_theory.limits.preserves_colimit_right_op CategoryTheory.Limits.preservesColimitRightOp
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.unop : C ⥤ D` preserves
colimits of `K : J ⥤ C`. -/
def preservesColimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimit K.op F] :
- PreservesColimit K F.unop
- where preserves {_} hc :=
+ PreservesColimit K F.unop where
+ preserves {_} hc :=
isColimitCoconeUnopOfCone _ (isLimitOfPreserves F (isLimitCoconeOp _ hc))
#align category_theory.limits.preserves_colimit_unop CategoryTheory.Limits.preservesColimitUnop
@@ -154,43 +155,43 @@ def preservesColimitsOfShapeUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimitsOfSha
end
/-- If `F : C ⥤ D` preserves colimits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits. -/
-def preservesLimitsOp (F : C ⥤ D) [PreservesColimits F] : PreservesLimits F.op
- where preservesLimitsOfShape {_} _ := preservesLimitsOfShapeOp _ _
+def preservesLimitsOp (F : C ⥤ D) [PreservesColimits F] : PreservesLimits F.op where
+ preservesLimitsOfShape {_} _ := preservesLimitsOfShapeOp _ _
#align category_theory.limits.preserves_limits_op CategoryTheory.Limits.preservesLimitsOp
/-- If `F : C ⥤ Dᵒᵖ` preserves colimits, then `F.left_op : Cᵒᵖ ⥤ D` preserves limits. -/
-def preservesLimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesColimits F] : PreservesLimits F.leftOp
- where preservesLimitsOfShape {_} _ := preservesLimitsOfShapeLeftOp _ _
+def preservesLimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesColimits F] : PreservesLimits F.leftOp where
+ preservesLimitsOfShape {_} _ := preservesLimitsOfShapeLeftOp _ _
#align category_theory.limits.preserves_limits_left_op CategoryTheory.Limits.preservesLimitsLeftOp
/-- If `F : Cᵒᵖ ⥤ D` preserves colimits, then `F.right_op : C ⥤ Dᵒᵖ` preserves limits. -/
-def preservesLimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesColimits F] : PreservesLimits F.rightOp
- where preservesLimitsOfShape {_} _ := preservesLimitsOfShapeRightOp _ _
+def preservesLimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesColimits F] : PreservesLimits F.rightOp where
+ preservesLimitsOfShape {_} _ := preservesLimitsOfShapeRightOp _ _
#align category_theory.limits.preserves_limits_right_op CategoryTheory.Limits.preservesLimitsRightOp
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits, then `F.unop : C ⥤ D` preserves limits. -/
-def preservesLimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimits F] : PreservesLimits F.unop
- where preservesLimitsOfShape {_} _ := preservesLimitsOfShapeUnop _ _
+def preservesLimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimits F] : PreservesLimits F.unop where
+ preservesLimitsOfShape {_} _ := preservesLimitsOfShapeUnop _ _
#align category_theory.limits.preserves_limits_unop CategoryTheory.Limits.preservesLimitsUnop
/-- If `F : C ⥤ D` preserves limits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits. -/
-def perservesColimitsOp (F : C ⥤ D) [PreservesLimits F] : PreservesColimits F.op
- where preservesColimitsOfShape {_} _ := preservesColimitsOfShapeOp _ _
+def perservesColimitsOp (F : C ⥤ D) [PreservesLimits F] : PreservesColimits F.op where
+ preservesColimitsOfShape {_} _ := preservesColimitsOfShapeOp _ _
#align category_theory.limits.perserves_colimits_op CategoryTheory.Limits.perservesColimitsOp
/-- If `F : C ⥤ Dᵒᵖ` preserves limits, then `F.left_op : Cᵒᵖ ⥤ D` preserves colimits. -/
-def preservesColimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesLimits F] : PreservesColimits F.leftOp
- where preservesColimitsOfShape {_} _ := preservesColimitsOfShapeLeftOp _ _
+def preservesColimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesLimits F] : PreservesColimits F.leftOp where
+ preservesColimitsOfShape {_} _ := preservesColimitsOfShapeLeftOp _ _
#align category_theory.limits.preserves_colimits_left_op CategoryTheory.Limits.preservesColimitsLeftOp
/-- If `F : Cᵒᵖ ⥤ D` preserves limits, then `F.right_op : C ⥤ Dᵒᵖ` preserves colimits. -/
-def preservesColimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesLimits F] : PreservesColimits F.rightOp
- where preservesColimitsOfShape {_} _ := preservesColimitsOfShapeRightOp _ _
+def preservesColimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesLimits F] : PreservesColimits F.rightOp where
+ preservesColimitsOfShape {_} _ := preservesColimitsOfShapeRightOp _ _
#align category_theory.limits.preserves_colimits_right_op CategoryTheory.Limits.preservesColimitsRightOp
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits, then `F.unop : C ⥤ D` preserves colimits. -/
-def preservesColimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimits F] : PreservesColimits F.unop
- where preservesColimitsOfShape {_} _ := preservesColimitsOfShapeUnop _ _
+def preservesColimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimits F] : PreservesColimits F.unop where
+ preservesColimitsOfShape {_} _ := preservesColimitsOfShapeUnop _ _
#align category_theory.limits.preserves_colimits_unop CategoryTheory.Limits.preservesColimitsUnop
end
@@ -203,56 +204,58 @@ variable {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₁} D]
/-- If `F : C ⥤ D` preserves finite colimits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite
limits. -/
-def preservesFiniteLimitsOp (F : C ⥤ D) [PreservesFiniteColimits F] : PreservesFiniteLimits F.op
- where preservesFiniteLimits J (_ : SmallCategory J) _ := preservesLimitsOfShapeOp J F
+def preservesFiniteLimitsOp (F : C ⥤ D) [PreservesFiniteColimits F] :
+ PreservesFiniteLimits F.op where
+ preservesFiniteLimits J (_ : SmallCategory J) _ := preservesLimitsOfShapeOp J F
#align category_theory.limits.preserves_finite_limits_op CategoryTheory.Limits.preservesFiniteLimitsOp
/-- If `F : C ⥤ Dᵒᵖ` preserves finite colimits, then `F.left_op : Cᵒᵖ ⥤ D` preserves finite
limits. -/
def preservesFiniteLimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesFiniteColimits F] :
- PreservesFiniteLimits F.leftOp
- where preservesFiniteLimits J (_ : SmallCategory J) _ := preservesLimitsOfShapeLeftOp J F
+ PreservesFiniteLimits F.leftOp where
+ preservesFiniteLimits J (_ : SmallCategory J) _ := preservesLimitsOfShapeLeftOp J F
#align category_theory.limits.preserves_finite_limits_left_op CategoryTheory.Limits.preservesFiniteLimitsLeftOp
/-- If `F : Cᵒᵖ ⥤ D` preserves finite colimits, then `F.right_op : C ⥤ Dᵒᵖ` preserves finite
limits. -/
def preservesFiniteLimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesFiniteColimits F] :
- PreservesFiniteLimits F.rightOp
- where preservesFiniteLimits J (_ : SmallCategory J) _ := preservesLimitsOfShapeRightOp J F
+ PreservesFiniteLimits F.rightOp where
+ preservesFiniteLimits J (_ : SmallCategory J) _ := preservesLimitsOfShapeRightOp J F
#align category_theory.limits.preserves_finite_limits_right_op CategoryTheory.Limits.preservesFiniteLimitsRightOp
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite colimits, then `F.unop : C ⥤ D` preserves finite
limits. -/
def preservesFiniteLimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesFiniteColimits F] :
- PreservesFiniteLimits F.unop
- where preservesFiniteLimits J (_ : SmallCategory J) _ := preservesLimitsOfShapeUnop J F
+ PreservesFiniteLimits F.unop where
+ preservesFiniteLimits J (_ : SmallCategory J) _ := preservesLimitsOfShapeUnop J F
#align category_theory.limits.preserves_finite_limits_unop CategoryTheory.Limits.preservesFiniteLimitsUnop
/-- If `F : C ⥤ D` preserves finite limits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite
colimits. -/
-def preservesFiniteColimitsOp (F : C ⥤ D) [PreservesFiniteLimits F] : PreservesFiniteColimits F.op
- where preservesFiniteColimits J (_ : SmallCategory J) _ := preservesColimitsOfShapeOp J F
+def preservesFiniteColimitsOp (F : C ⥤ D) [PreservesFiniteLimits F] :
+ PreservesFiniteColimits F.op where
+ preservesFiniteColimits J (_ : SmallCategory J) _ := preservesColimitsOfShapeOp J F
#align category_theory.limits.preserves_finite_colimits_op CategoryTheory.Limits.preservesFiniteColimitsOp
/-- If `F : C ⥤ Dᵒᵖ` preserves finite limits, then `F.left_op : Cᵒᵖ ⥤ D` preserves finite
colimits. -/
def preservesFiniteColimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesFiniteLimits F] :
- PreservesFiniteColimits F.leftOp
- where preservesFiniteColimits J (_ : SmallCategory J) _ := preservesColimitsOfShapeLeftOp J F
+ PreservesFiniteColimits F.leftOp where
+ preservesFiniteColimits J (_ : SmallCategory J) _ := preservesColimitsOfShapeLeftOp J F
#align category_theory.limits.preserves_finite_colimits_left_op CategoryTheory.Limits.preservesFiniteColimitsLeftOp
/-- If `F : Cᵒᵖ ⥤ D` preserves finite limits, then `F.right_op : C ⥤ Dᵒᵖ` preserves finite
colimits. -/
def preservesFiniteColimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesFiniteLimits F] :
- PreservesFiniteColimits F.rightOp
- where preservesFiniteColimits J (_ : SmallCategory J) _ := preservesColimitsOfShapeRightOp J F
+ PreservesFiniteColimits F.rightOp where
+ preservesFiniteColimits J (_ : SmallCategory J) _ := preservesColimitsOfShapeRightOp J F
#align category_theory.limits.preserves_finite_colimits_right_op CategoryTheory.Limits.preservesFiniteColimitsRightOp
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite limits, then `F.unop : C ⥤ D` preserves finite
colimits. -/
def preservesFiniteColimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesFiniteLimits F] :
- PreservesFiniteColimits F.unop
- where preservesFiniteColimits J (_ : SmallCategory J) _ := preservesColimitsOfShapeUnop J F
+ PreservesFiniteColimits F.unop where
+ preservesFiniteColimits J (_ : SmallCategory J) _ := preservesColimitsOfShapeUnop J F
#align category_theory.limits.preserves_finite_colimits_unop CategoryTheory.Limits.preservesFiniteColimitsUnop
end
@@ -2,15 +2,12 @@
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.limits.preserves.opposites
-! leanprover-community/mathlib commit 9ed4366659f4fcca0ee70310d26ac5518dcb6dd0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Limits.Opposites
import Mathlib.CategoryTheory.Limits.Preserves.Finite
+#align_import category_theory.limits.preserves.opposites from "leanprover-community/mathlib"@"9ed4366659f4fcca0ee70310d26ac5518dcb6dd0"
+
/-!
# Limit preservation properties of `functor.op` and related constructions
The unported dependencies are