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.
- 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.
Cites5
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.Homproof · cited by 32,603
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- Quiver.Pathproof · cited by 166
- CategoryTheory.Pathsstatement and proof · cited by 82
Cited by13
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.composePath_memstatement and proof · cited by 2
- CategoryTheory.MorphismProperty.toPath_mem_pathsstatement · cited by 1
- CategoryTheory.MorphismProperty.comp_mem_paths_iffstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.composePath_mem_of_id_memstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.monotone_pathsstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.nil_mem_pathsstatement · cited by 0
- CategoryTheory.MorphismProperty.toPath_mem_paths_iffstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.comp_mem_paths_iff'statement · cited by 0
- CategoryTheory.MorphismProperty.composePath_mem_of_length_posstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.cons_mem_pathsstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.cons_mem_paths_iffstatement · cited by 0
- CategoryTheory.MorphismProperty.paths_le_inverseImagestatement · cited by 0