Theorems · Definition · category theory

CategoryTheory.Limits.Cocone.op

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F : CategoryTheory.Functor J C} → CategoryTheory.Limits.Cocone F → CategoryTheory.Limits.Cone F.op

Change a Cocone F into a Cone F.op.

Defined in: Mathlib.CategoryTheory.Limits.Cones
Cited by: 38 results in Mathlib
Foundations: Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category

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Dashed lines are statement dependencies; solid lines are citations in proofs.

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.Functorstatement and proof · cited by 16,252
Oppositestatement · cited by 8,081
CategoryTheory.Limits.Cocone.ptproof · cited by 1,354
CategoryTheory.Functor.opstatement · cited by 997
CategoryTheory.Limits.Coconestatement and proof · cited by 746
CategoryTheory.Limits.Conestatement · cited by 710
CategoryTheory.Limits.Cocone.ιproof · cited by 605
CategoryTheory.NatTrans.opproof · cited by 41

Cited by70

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.IsColimit.opstatement and proof · cited by 14
CategoryTheory.Limits.PushoutCocone.opproof · cited by 7
CategoryTheory.Limits.isColimitOfOpstatement and proof · cited by 7
CategoryTheory.Limits.coconeOpEquivproof · cited by 6
CategoryTheory.Presheaf.isSheaf_iff_isLimitstatement and proof · cited by 6
CategoryTheory.Limits.PushoutCocone.op_π_appstatement · cited by 5
CategoryTheory.Limits.Cofork.opproof · cited by 5
CategoryTheory.Limits.limitOpIsoOpColimitproof · cited by 5
CategoryTheory.Limits.PushoutCocone.isColimitEquivIsLimitOpproof · cited by 5
CategoryTheory.Limits.Cofan.IsColimit.opproof · cited by 4
CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_πproof · cited by 3
TopCat.Presheaf.IsSheafPairwiseIntersectionsproof · cited by 3