Theorems · Definition · category theory

TopPair.Homotopy.casesOn

{X Y : TopPair} →
  {f g : X ⟶ Y} →
    {motive : TopPair.Homotopy f g → Sort u_1} →
      (t : TopPair.Homotopy f g) →
        ((fst : TopCat.Homotopy (TopPair.Hom.fst f) (TopPair.Hom.fst g)) →
            (snd : TopCat.Homotopy (TopPair.Hom.snd f) (TopPair.Hom.snd g)) →
              (w :
                  CategoryTheory.CategoryStruct.comp
                      (CategoryTheory.MonoidalCategoryStruct.whiskerRight TopPair.map TopCat.I) fst.h =
                    CategoryTheory.CategoryStruct.comp snd.h TopPair.map) →
                motive { fst := fst, snd := snd, w := w }) →
          motive t

Defined in: Mathlib.Topology.Category.TopPair
Cited by: 0 results in Mathlib
Foundations: Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites19

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Top.topstatement · cited by 9,680
CategoryTheory.Functor.idstatement · cited by 3,333
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
CategoryTheory.MorphismPropertystatement · cited by 2,179
TopCatstatement · cited by 1,889
CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement and proof · cited by 903
TopPairstatement and proof · cited by 67
TopCat.isEmbeddingstatement · cited by 67
TopCat.Istatement and proof · cited by 64
TopPair.fststatement · cited by 21

Cited by2

Results whose statement or proof uses this declaration.

TopPair.Homotopy.noConfusionproof · cited by 0
TopPair.Homotopy.noConfusionTypeproof · cited by 0