Theorems · Definition · category theory
CategoryTheory.Limits.walkingParallelPairOpEquiv
CategoryTheory.Limits.WalkingParallelPair ≌ CategoryTheory.Limits.WalkingParallelPairᵒᵖ
The equivalence WalkingParallelPair ⥤ WalkingParallelPairᵒᵖ sending left to left and right to
right.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Limits.WalkingParallelPairstatement and proof · cited by 781
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.Functor.leftOpproof · cited by 187
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.eqToIsoproof · cited by 97
- CategoryTheory.Limits.walkingParallelPairOpproof · cited by 11
Cited by31
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.parallelPairOpIsostatement and proof · cited by 9
- CategoryTheory.Limits.Fork.opproof · cited by 7
- CategoryTheory.Limits.Cofork.opproof · cited by 5
- CategoryTheory.Limits.Cofork.unopproof · cited by 5
- CategoryTheory.Limits.Fork.unopproof · cited by 5
- CategoryTheory.Limits.opParallelPairIsostatement and proof · cited by 4
- CategoryTheory.Limits.opParallelPairIso_hom_app_zerostatement and proof · cited by 2
- CategoryTheory.Limits.opParallelPairIso_inv_app_onestatement and proof · cited by 2
- CategoryTheory.Limits.opParallelPairIso_hom_app_onestatement and proof · cited by 1
- CategoryTheory.Limits.opParallelPairIso_inv_app_zerostatement and proof · cited by 1
- CategoryTheory.Limits.Cofork.isColimitEquivIsLimitOpproof · cited by 0
- CategoryTheory.Limits.Cofork.isColimitEquivIsLimitUnopproof · cited by 0