Theorems · Theorem · category theory

CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {S : CategoryTheory.Functor C D} {T : D} {A : CategoryTheory.CostructuredArrow S T}
  {P : (CategoryTheory.CostructuredArrow S T)ᵒᵖ} (f : P ⟶ Opposite.op A) [inst_2 : CategoryTheory.Mono f.unop.left.op],
  CategoryTheory.CategoryStruct.comp f.unop.left (CategoryTheory.Subobject.underlyingIso f.unop.left.op).hom.unop =
    (CategoryTheory.Subobject.mk f.unop.left.op).arrow.unop

Technical lemma for lift_projectQuotient.

Defined in

Mathlib.CategoryTheory.Subobject.Comma

Cited by

1 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Mono