Documentation
Mathlib
.
CategoryTheory
.
Abelian
.
GrothendieckAxioms
.
SheafOfModules
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Imports
Init
Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.PresheafOfModules
Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian
Mathlib.Algebra.Category.ModuleCat.Sheaf.Colimits
Imported by
SheafOfModules
.
instIsGrothendieckAbelian
The category of sheaves of modules is Grothendieck abelian
#
source
instance
SheafOfModules
.
instIsGrothendieckAbelian
{
C
:
Type
u}
[
CategoryTheory.SmallCategory
C
]
{
J
:
CategoryTheory.GrothendieckTopology
C
}
(
R
:
CategoryTheory.Sheaf
J
RingCat
)
:
CategoryTheory.IsGrothendieckAbelian.{u, u, u + 1}
(
SheafOfModules
R
)