Theorems · Theorem · category theory

CategoryTheory.Idempotents.functorExtension_obj_map

∀ (C : Type u_1) (D : Type u_2) [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.IsIdempotentComplete D]
  (X : CategoryTheory.Functor C D) {X_1 Y : CategoryTheory.Idempotents.Karoubi C} (f : X_1 ⟶ Y),
  ((CategoryTheory.Idempotents.functorExtension C D).obj X).map f =
    (CategoryTheory.Idempotents.toKaroubiEquivalence D).inverse.map
      (((CategoryTheory.Idempotents.functorExtension₂ C D).obj X).map f)

Defined in

Mathlib.CategoryTheory.Idempotents.FunctorExtension

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsIdempotentComplete