Theorems · Theorem · category theory

CategoryTheory.eqToHom_map

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) {X Y : C} (p : X = Y), F.map (CategoryTheory.eqToHom p) = CategoryTheory.eqToHom ⋯

This is not always a good idea as a @[simp] lemma, as we lose the ability to use results that interact with F, e.g. the naturality of a natural transformation. In some files it may be appropriate to use attribute [local simp] eqToHom_map, however.

Defined in

Mathlib.CategoryTheory.EqToHom

Cited by

29 results in Mathlib

Foundations

Depth 6 from the axioms · uses propext

Assumes

CategoryTheory.CategoryCategoryTheory.Category