Theorems · Theorem · category theory
SimplexCategory.len_le_of_epi
∀ {x y : SimplexCategory} (f : x ⟶ y) [CategoryTheory.Epi f], y.len ≤ x.lenAn epimorphism in SimplexCategory must decrease lengths
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Epi
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.Epistatement and proof · cited by 688
- 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_surjectiveproof · cited by 10
- SimplexCategory.epi_iff_surjectiveproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- SSet.mem_skeletonproof · cited by 4
- SimplexCategory.len_eq_of_isIsoproof · cited by 3
- SimplexCategory.Truncated.morphismProperty_eq_topproof · cited by 2
- CategoryTheory.SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zeroproof · cited by 2
- SimplexCategory.le_of_epiproof · cited by 1
- SimplexCategory.image_eqproof · cited by 1
- SSet.boundary_obj_eq_univproof · cited by 1
- SSet.isIso_of_nonDegenerateproof · cited by 1
- CategoryTheory.SimplicialObject.Splitting.IndexSet.eqId_iff_len_leproof · cited by 1