Theorems · Theorem · category theory

CategoryTheory.Quotient.functor_map_eq_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (r : HomRel C) [h : CategoryTheory.Congruence r]
  {X Y : C} (f f' : X ⟶ Y),
  (CategoryTheory.Quotient.functor r).map f = (CategoryTheory.Quotient.functor r).map f' ↔ r f f'

Defined in

Mathlib.CategoryTheory.Quotient

Cited by

2 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Congruence