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Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.composePath_mem_of_id_mem

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (W : CategoryTheory.MorphismProperty C)
  [W.IsStableUnderComposition] {X Y : C} {p : Quiver.Path X Y},
  W.paths p → W (CategoryTheory.CategoryStruct.id X) → W (CategoryTheory.composePath p)
Defined in
Mathlib.CategoryTheory.PathCategory.MorphismProperty
Cited by
1 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext
Assumes
CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsStableUnderComposition
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CategoryTheory.MorphismProperty.composePath_mem · cited by 2MorphismProperty.composeP…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…Quiver.Path · cited by 166Quiver.PathCategoryTheory.MorphismProperty.IsStableUnderComposition · cited by 84MorphismProperty.IsStable…CategoryTheory.MorphismProperty.comp_mem · cited by 48MorphismProperty.comp_memCategoryTheory.composePath · cited by 16CategoryTheory.composePathCategoryTheory.MorphismProperty.paths · cited by 13MorphismProperty.pathsMorphismProperty.composePath_…CITED BYCITES

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