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Theorems · Definition · category theory

CategoryTheory.MorphismProperty.paths

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    CategoryTheory.MorphismProperty C → CategoryTheory.MorphismProperty (CategoryTheory.Paths C)

For any morphism property W on C, W.paths is the morphism property on Paths C containing all paths of morphisms in W.

Defined in
Mathlib.CategoryTheory.PathCategory.MorphismProperty
Cited by
13 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.MorphismProperty.composePath_mem · cited by 2MorphismProperty.composeP…CategoryTheory.MorphismProperty.toPath_mem_paths · cited by 1MorphismProperty.toPath_m…CategoryTheory.MorphismProperty.comp_mem_paths_iff · cited by 1MorphismProperty.comp_mem…CategoryTheory.MorphismProperty.composePath_mem_of_id_mem · cited by 1MorphismProperty.composeP…CategoryTheory.MorphismProperty.monotone_paths · cited by 1MorphismProperty.monotone…CategoryTheory.MorphismProperty.nil_mem_paths · cited by 0MorphismProperty.nil_mem_…CategoryTheory.MorphismProperty.toPath_mem_paths_iff · cited by 0MorphismProperty.toPath_m…CategoryTheory.MorphismProperty.comp_mem_paths_iff' · cited by 0MorphismProperty.comp_mem…CategoryTheory.MorphismProperty.composePath_mem_of_length_pos · cited by 0MorphismProperty.composeP…CategoryTheory.MorphismProperty.cons_mem_paths · cited by 0MorphismProperty.cons_mem…CategoryTheory.MorphismProperty.cons_mem_paths_iff · cited by 0MorphismProperty.cons_mem…CategoryTheory.MorphismProperty.paths_le_inverseImage · cited by 0MorphismProperty.paths_le…CategoryTheory.MorphismProperty.multiplicativeClosure_eq_strictMap_paths · cited by 0MorphismProperty.multipli…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…Quiver.Path · cited by 166Quiver.PathCategoryTheory.Paths · cited by 82CategoryTheory.PathsMorphismProperty.pathsCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by13

Results whose statement or proof uses this declaration.