Theorems · Theorem · category theory

CategoryTheory.SingleFunctors.postcompIsoOfIso_hom_hom_app

∀ {C : Type u_1} {D : Type u_2} {E : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Category.{v_3, u_3} E] {A : Type u_5}
  [inst_3 : AddMonoid A] [inst_4 : CategoryTheory.HasShift D A] [inst_5 : CategoryTheory.HasShift E A]
  (F : CategoryTheory.SingleFunctors C D A) {G G' : CategoryTheory.Functor D E} (e : G ≅ G') [inst_6 : G.CommShift A]
  [inst_7 : G'.CommShift A] [inst_8 : CategoryTheory.NatTrans.CommShift e.hom A] (a : A) (X : C),
  ((F.postcompIsoOfIso e).hom.hom a).app X = e.hom.app ((F.functor a).obj X)

Defined in

Mathlib.CategoryTheory.Shift.SingleFunctors

Cited by

0 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Functor.CommShiftCategoryTheory.NatTrans.CommShift