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- Cited by
- 7 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Limits.prodstatement · cited by 364
- CategoryTheory.Limits.limit.lift_πproof · cited by 266
- CategoryTheory.Limits.prod.sndstatement · cited by 185
- CategoryTheory.Limits.HasBinaryProductstatement and proof · cited by 169
- CategoryTheory.Limits.BinaryFan.mkproof · cited by 112
- HomotopicalAlgebra.PrepathObject.Pstatement · cited by 76
- HomotopicalAlgebra.PrepathObjectstatement and proof · cited by 56
- HomotopicalAlgebra.PrepathObject.p₀proof · cited by 40
- HomotopicalAlgebra.PrepathObject.p₁statement and proof · cited by 40
Cited by7
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.RightHomotopyRel.exists_very_good_pathObjectproof · cited by 3
- HomotopicalAlgebra.PrepathObject.symm_pproof · cited by 2
- HomotopicalAlgebra.PathObject.RightHomotopy.exists_good_pathObjectproof · cited by 1
- HomotopicalAlgebra.RightHomotopyRel.postcompproof · cited by 0
- HomotopicalAlgebra.PathObject.ofFactorizationData_pproof · cited by 0
- HomotopicalAlgebra.PrepathObject.p_snd_assocproof · cited by 0