Theorems · Definition · category theory

HomotopicalAlgebra.PathObject.symm

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {A : C} →
      [inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] →
        HomotopicalAlgebra.PathObject A → HomotopicalAlgebra.PathObject A

The path object obtained by switching the two projections.

Defined in: Mathlib.AlgebraicTopology.ModelCategory.PathObject
Cited by: 6 results in Mathlib
Foundations: Depth 12 from the axioms · uses propext
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithWeakEquivalences

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Cites6

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
HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement and proof · cited by 77
HomotopicalAlgebra.PrepathObjectproof · cited by 56
HomotopicalAlgebra.PathObjectstatement and proof · cited by 32
HomotopicalAlgebra.PathObject.toPrepathObjectproof · cited by 24
HomotopicalAlgebra.PrepathObject.symmproof · cited by 7

Cited by7

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.PathObject.symm_pstatement · cited by 1
HomotopicalAlgebra.PathObject.RightHomotopy.symmstatement · cited by 1
HomotopicalAlgebra.PathObject.symm_Pstatement and proof · cited by 0
HomotopicalAlgebra.PathObject.symm_p_assocstatement · cited by 0
HomotopicalAlgebra.PathObject.symm_p₀statement and proof · cited by 0
HomotopicalAlgebra.PathObject.symm_p₁statement and proof · cited by 0
HomotopicalAlgebra.PathObject.symm_ιstatement and proof · cited by 0