Theorems · Theorem · category theory
CategoryTheory.Idempotents.functorExtension_obj_obj
∀ (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 : CategoryTheory.Idempotents.Karoubi C),
((CategoryTheory.Idempotents.functorExtension C D).obj X).obj X_1 =
(CategoryTheory.Idempotents.toKaroubiEquivalence D).inverse.obj
(((CategoryTheory.Idempotents.functorExtension₂ C D).obj X).obj X_1)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Equivalence.inversestatement · cited by 1,130
- CategoryTheory.Idempotents.Karoubistatement and proof · cited by 233
- CategoryTheory.IsIdempotentCompletestatement and proof · cited by 29
- CategoryTheory.Idempotents.functorExtension₂statement · cited by 15
- CategoryTheory.Idempotents.toKaroubiEquivalencestatement · cited by 14
- CategoryTheory.Idempotents.functorExtensionstatement and proof · cited by 4
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