Theorems · Definition · category theory

CategoryTheory.Limits.PullbackCone.isoMk

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {F : CategoryTheory.Functor CategoryTheory.Limits.WalkingCospan C} →
      (t : CategoryTheory.Limits.Cone F) →
        (CategoryTheory.Limits.Cone.postcompose (CategoryTheory.Limits.diagramIsoCospan F).hom).obj t ≅
          CategoryTheory.Limits.PullbackCone.mk (t.π.app CategoryTheory.Limits.WalkingCospan.left)
            (t.π.app CategoryTheory.Limits.WalkingCospan.right) ⋯

A diagram WalkingCospan ⥤ C is isomorphic to some PullbackCone.mk after composing with diagramIsoCospan.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone
Cited by: 4 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites27

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
Quiver.Homstatement · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.mapstatement · cited by 8,698
CategoryTheory.Iso.homstatement and proof · cited by 7,684
CategoryTheory.NatTrans.appstatement · cited by 7,406
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
CategoryTheory.Functor.conststatement · cited by 1,264

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.IsPullback.of_isLimit_coneproof · cited by 1
CategoryTheory.Limits.PullbackCone.isoMk_hom_homstatement and proof · cited by 0
CategoryTheory.Limits.PullbackCone.isoMk_inv_homstatement and proof · cited by 0
CategoryTheory.Limits.preservesPullback_symmetryproof · cited by 0