Theorems · Definition · category theory

CategoryTheory.eqToHom

{C : Type u₁} → [inst : CategoryTheory.CategoryStruct.{v₁, u₁} C] → {X Y : C} → X = Y → (X ⟶ Y)

An equality X = Y gives us a morphism X ⟶ Y. It is typically better to use this, rather than rewriting by the equality then using 𝟙 _ which usually leads to dependent type theory hell.

Defined in

Mathlib.CategoryTheory.EqToHom

Cited by

860 results in Mathlib

Foundations

Depth 5 from the axioms, rests on 10 definitions · uses no axioms

Assumes

CategoryTheory.CategoryStruct