Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Comma.mapLeftIso_inverse_obj_hom

∀ {A : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} A] {B : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_2, u_2} B] {T : Type u_3} [inst_2 : CategoryTheory.Category.{v_3, u_3} T]
  (R : CategoryTheory.Functor B T) {P : CategoryTheory.MorphismProperty T} {Q : CategoryTheory.MorphismProperty A}
  {W : CategoryTheory.MorphismProperty B} [inst_3 : Q.IsMultiplicative] [inst_4 : W.IsMultiplicative]
  {L₁ L₂ : CategoryTheory.Functor A T} [inst_5 : P.RespectsIso] [inst_6 : Q.RespectsIso] [inst_7 : W.RespectsIso]
  (e : L₁ ≅ L₂) (X : CategoryTheory.MorphismProperty.Comma L₂ R P Q W),
  ((CategoryTheory.MorphismProperty.Comma.mapLeftIso R e).inverse.obj X).hom =
    CategoryTheory.CategoryStruct.comp (e.hom.app X.left) X.hom

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.RespectsIsoCategoryTheory.MorphismProperty.RespectsIsoCategoryTheory.MorphismProperty.RespectsIso