Theorems · Theorem · category theory
CategoryTheory.Equivalence.symmEquivInverse_obj_inverse
∀ (C : Type u_1) [inst : CategoryTheory.Category.{v_1, u_1} C] (D : Type u_2)
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] (X : (D ≌ C)ᵒᵖ),
((CategoryTheory.Equivalence.symmEquivInverse C D).obj X).inverse = (Opposite.unop X).functor- Cited by
- 0 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- Opposite.unopstatement · cited by 2,231
- CategoryTheory.Equivalence.functorstatement · cited by 1,268
- CategoryTheory.Equivalence.inversestatement and proof · cited by 1,130
- CategoryTheory.Equivalencestatement and proof · cited by 601
- CategoryTheory.Equivalence.symmEquivInversestatement and proof · cited by 10
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