Theorems · Theorem · category theory

SheafOfModules.freeHomEquiv_symm_comp

∀ {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} (s : I → M.sections)
  (p : M ⟶ N),
  CategoryTheory.CategoryStruct.comp (M.freeHomEquiv.symm s) p =
    N.freeHomEquiv.symm fun i => SheafOfModules.sectionsMap p (s i)

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Free

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijective