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Theorems · Theorem · category theory

HomotopicalAlgebra.PrepathObject.symm_p

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A : C} (P : HomotopicalAlgebra.PrepathObject A)
  [inst_1 : CategoryTheory.Limits.HasBinaryProducts C],
  P.symm.p = CategoryTheory.CategoryStruct.comp P.p (CategoryTheory.Limits.prod.braiding A A).hom
Defined in
Mathlib.AlgebraicTopology.ModelCategory.PathObject
Cited by
2 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProducts
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Around this declaration

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HomotopicalAlgebra.PathObject.symm_p · cited by 1PathObject.symm_pHomotopicalAlgebra.PrepathObject.symm_p_assoc · cited by 0PrepathObject.symm_p_assocCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Limits.pair · cited by 536Limits.pairCategoryTheory.Limits.prod · cited by 364Limits.prodCategoryTheory.Limits.prod.fst · cited by 189prod.fstCategoryTheory.Limits.prod.snd · cited by 185prod.sndCategoryTheory.Limits.prod.lift · cited by 123prod.liftCategoryTheory.Limits.HasBinaryProducts · cited by 79Limits.HasBinaryProductsHomotopicalAlgebra.PrepathObject.P · cited by 76PrepathObject.PHomotopicalAlgebra.PrepathObject · cited by 56HomotopicalAlgebra.Prepat…CategoryTheory.Limits.prod.comp_lift · cited by 46prod.comp_liftPrepathObject.symm_pCITED BYCITES

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