Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.composePath_mem_of_length_pos
∀ {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 → 0 < p.length → W (CategoryTheory.composePath p)- Cited by
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- Foundations
- Depth 21 from the axioms · uses propext
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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.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Category.id_compproof · cited by 1,998
- Quiver.Pathstatement and proof · cited by 166
- CategoryTheory.MorphismProperty.IsStableUnderCompositionstatement and proof · cited by 84
- CategoryTheory.MorphismProperty.comp_memproof · cited by 48
- Quiver.Path.lengthstatement and proof · cited by 39
- CategoryTheory.composePathstatement and proof · cited by 16
- CategoryTheory.MorphismProperty.pathsstatement and proof · cited by 13
- Quiver.Path.casesOnproof · cited by 12
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