Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Under.forget_comp_forget_map

∀ {T : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} T] (P Q : CategoryTheory.MorphismProperty T) (X : T)
  [inst_1 : Q.IsMultiplicative] {A B : P.Under Q X} (f : A ⟶ B),
  ((CategoryTheory.MorphismProperty.Under.forget P Q X).comp (CategoryTheory.Under.forget X)).map f = f.right

Occasionally useful for rewriting in the backwards direction.

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

0 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicative