mathlib documentation


Isomorphisms about functors which preserve (co)limits #

If G preserves limits, and C and D have limits, then for any diagram F : J ⥤ C we have a canonical isomorphism preserves_limit_iso : G.obj (limit F) ≅ limit (F ⋙ G). We also show that we can commute is_limit.lift of a preserved limit with functor.map_cone: (preserves_limit.preserves t).lift (G.map_cone c₂) = (t.lift c₂).

The duals of these are also given. For functors which preserve (co)limits of specific shapes, see preserves/shapes.lean.