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Theorems · Theorem · category theory

HomotopicalAlgebra.PrepathObject.p_snd

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A : C} (P : HomotopicalAlgebra.PrepathObject A)
  [inst_1 : CategoryTheory.Limits.HasBinaryProduct A A],
  CategoryTheory.CategoryStruct.comp P.p CategoryTheory.Limits.prod.snd = P.p₁
Defined in
Mathlib.AlgebraicTopology.ModelCategory.PathObject
Cited by
7 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProduct

Around this declaration

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

HomotopicalAlgebra.RightHomotopyClass.precomp_bijective_of_cofibration_of_weakEquivalence · cited by 4RightHomotopyClass.precom…HomotopicalAlgebra.RightHomotopyRel.exists_very_good_pathObject · cited by 3RightHomotopyRel.exists_v…HomotopicalAlgebra.PrepathObject.symm_p · cited by 2PrepathObject.symm_pHomotopicalAlgebra.PathObject.RightHomotopy.exists_good_pathObject · cited by 1RightHomotopy.exists_good…HomotopicalAlgebra.RightHomotopyRel.postcomp · cited by 0RightHomotopyRel.postcompHomotopicalAlgebra.PathObject.ofFactorizationData_p · cited by 0PathObject.ofFactorizatio…HomotopicalAlgebra.PrepathObject.p_snd_assoc · cited by 0PrepathObject.p_snd_assocCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Limits.prod · cited by 364Limits.prodCategoryTheory.Limits.limit.lift_π · cited by 266limit.lift_πCategoryTheory.Limits.prod.snd · cited by 185prod.sndCategoryTheory.Limits.HasBinaryProduct · cited by 169Limits.HasBinaryProductCategoryTheory.Limits.BinaryFan.mk · cited by 112BinaryFan.mkHomotopicalAlgebra.PrepathObject.P · cited by 76PrepathObject.PHomotopicalAlgebra.PrepathObject · cited by 56HomotopicalAlgebra.Prepat…HomotopicalAlgebra.PrepathObject.p₀ · cited by 40PrepathObject.p₀HomotopicalAlgebra.PrepathObject.p₁ · cited by 40PrepathObject.p₁HomotopicalAlgebra.PrepathObject.p · cited by 13PrepathObject.pPrepathObject.p_sndCITED BYCITES

Cites13

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Cited by7

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