Theorems · Theorem · category theory

TopPair.Homotopy.w

∀ {X Y : TopPair} {f g : X ⟶ Y} (self : TopPair.Homotopy f g),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight TopPair.map TopCat.I)
      self.fst.h =
    CategoryTheory.CategoryStruct.comp self.snd.h TopPair.map

The proof that the homotopies fit into a commutative square with the maps of the pairs.

Defined in: Mathlib.Topology.Category.TopPair
Cited by: 2 results in Mathlib
Foundations: Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites20

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 · 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 · cited by 903
TopPairstatement and proof · cited by 67
TopCat.isEmbeddingstatement · cited by 67
TopCat.Istatement · cited by 64
TopPair.fststatement · cited by 21

Cited by2

Results whose statement or proof uses this declaration.

TopPair.Homotopy.w_applyproof · cited by 1
TopPair.Homotopy.w_assocproof · cited by 0