Theorems · Theorem · category theory

SheafOfModules.freeHomEquiv_comp_apply

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : CategoryTheory.GrothendieckTopology C}
  {R : CategoryTheory.Sheaf J RingCat} [inst_1 : CategoryTheory.HasWeakSheafify J AddCommGrpCat]
  [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat] {M N : SheafOfModules R} {I : Type u}
  (f : SheafOfModules.free I ⟶ M) (p : M ⟶ N) (i : I),
  N.freeHomEquiv (CategoryTheory.CategoryStruct.comp f p) i = SheafOfModules.sectionsMap p (M.freeHomEquiv f i)

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Free

Cited by

0 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijective