Theorems · Theorem · category theory
SimplexCategory.len_le_of_mono
∀ {x y : SimplexCategory} (f : x ⟶ y) [CategoryTheory.Mono f], x.len ≤ y.lenA monomorphism in SimplexCategory must increase lengths
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Mono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- SimplexCategorystatement and proof · cited by 2,204
- CategoryTheory.Monostatement and proof · cited by 893
- SimplexCategory.lenstatement and proof · cited by 542
- Fintype.card_finproof · cited by 270
- SimplexCategory.Hom.toOrderHomproof · cited by 111
- OrderHom.toFunproof · cited by 45
- Fintype.card_le_of_injectiveproof · cited by 19
- SimplexCategory.mono_iff_injectiveproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- SimplexCategory.len_eq_of_isIsoproof · cited by 3
- SimplexCategory.le_of_monoproof · cited by 2
- SimplexCategory.Truncated.morphismProperty_eq_topproof · cited by 2
- CategoryTheory.SimplicialObject.Splitting.IndexSet.eqId_iff_monoproof · cited by 2
- SSet.mem_degenerate_iffproof · cited by 2
- SimplexCategory.image_eqproof · cited by 1
- SSet.N.dim_le_of_leproof · cited by 1
- SSet.mem_skeleton_obj_iff_of_nonDegenerateproof · cited by 1