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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.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Equalizers
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.

CategoryTheory.Limits.parallelPairOpIso · cited by 9Limits.parallelPairOpIsoCategoryTheory.Limits.Fork.op · cited by 7Fork.opCategoryTheory.Limits.Cofork.op · cited by 5Cofork.opCategoryTheory.Limits.Cofork.unop · cited by 5Cofork.unopCategoryTheory.Limits.Fork.unop · cited by 5Fork.unopCategoryTheory.Limits.opParallelPairIso · cited by 4Limits.opParallelPairIsoCategoryTheory.Limits.opParallelPairIso_hom_app_zero · cited by 2Limits.opParallelPairIso_…CategoryTheory.Limits.opParallelPairIso_inv_app_one · cited by 2Limits.opParallelPairIso_…CategoryTheory.Limits.opParallelPairIso_hom_app_one · cited by 1Limits.opParallelPairIso_…CategoryTheory.Limits.opParallelPairIso_inv_app_zero · cited by 1Limits.opParallelPairIso_…CategoryTheory.Limits.Cofork.isColimitEquivIsLimitOp · cited by 0Cofork.isColimitEquivIsLi…CategoryTheory.Limits.Cofork.isColimitEquivIsLimitUnop · cited by 0Cofork.isColimitEquivIsLi…CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_one · cited by 0Limits.walkingParallelPai…CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_zero · cited by 0Limits.walkingParallelPai…CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_one · cited by 0Limits.walkingParallelPai…Quiver.Hom · cited by 32603Quiver.HomOpposite · cited by 8081OppositeCategoryTheory.Limits.WalkingParallelPair · cited by 781Limits.WalkingParallelPairCategoryTheory.Equivalence · cited by 601CategoryTheory.EquivalenceCategoryTheory.Functor.leftOp · cited by 187Functor.leftOpCategoryTheory.NatIso.ofComponents · cited by 178NatIso.ofComponentsCategoryTheory.eqToIso · cited by 97CategoryTheory.eqToIsoCategoryTheory.Limits.walkingParallelPairOp · cited by 11Limits.walkingParallelPai…Limits.walkingParallelPairOpE…CITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by31

Results whose statement or proof uses this declaration.