Theorems · Definition · category theory
CategoryTheory.ShortComplex.opEquiv
(C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
(CategoryTheory.ShortComplex C)ᵒᵖ ≌ CategoryTheory.ShortComplex CᵒᵖThe obvious equivalence of categories (ShortComplex C)ᵒᵖ ≌ ShortComplex Cᵒᵖ.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.ShortComplex.opFunctorproof · cited by 8
- CategoryTheory.ShortComplex.unopFunctorproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.SnakeInput.opproof · cited by 10
- CategoryTheory.ShortComplex.opEquiv_counitIsostatement and proof · cited by 0
- CategoryTheory.ShortComplex.opEquiv_functorstatement and proof · cited by 0
- CategoryTheory.ShortComplex.opEquiv_inversestatement and proof · cited by 0
- CategoryTheory.ShortComplex.opEquiv_unitIsostatement and proof · cited by 0
- CategoryTheory.ShortComplex.unopOpproof · cited by 0
- CategoryTheory.ShortComplex.opUnopproof · cited by 0