Theorems · Theorem · category theory

CategoryTheory.ShortComplex.FunctorEquivalence.functor_obj_map

∀ (J : Type u_1) (C : Type u_2) [inst : CategoryTheory.Category.{v_1, u_1} J]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C] [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C]
  (S : CategoryTheory.ShortComplex (CategoryTheory.Functor J C)) {X Y : J} (f : X ⟶ Y),
  ((CategoryTheory.ShortComplex.FunctorEquivalence.functor J C).obj S).map f =
    S.mapNatTrans ((CategoryTheory.evaluation J C).map f)

Defined in

Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms