Theorems · Theorem · category theory
SimplexCategory.mono_iff_injective
∀ {n m : SimplexCategory} {f : n ⟶ m}, CategoryTheory.Mono f ↔ Function.Injective ⇑(SimplexCategory.Hom.toOrderHom f)A morphism in SimplexCategory is a monomorphism precisely when it is an injective function
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- SimplexCategorystatement and proof · cited by 2,204
- CategoryTheory.Equivalence.functorproof · cited by 1,268
- OrderHomstatement · cited by 934
- CategoryTheory.Monostatement · cited by 893
- SimplexCategory.lenstatement · cited by 542
- CategoryTheory.ConcreteCategory.hom_ofHomproof · cited by 205
- SimplexCategory.Hom.toOrderHomstatement and proof · cited by 111
- NonemptyFinLinOrd.ofHomproof · cited by 11
- CategoryTheory.Functor.mono_map_iff_monoproof · cited by 3
- SimplexCategory.skeletalEquivalenceproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- SimplexCategory.len_le_of_monoproof · cited by 8
- SSet.stdSimplex.mem_nonDegenerate_iff_monoproof · cited by 3
- AlgebraicTopology.DoldKan.degeneracy_comp_PInftyproof · cited by 2
- SimplexCategory.Truncated.morphismProperty_eq_topproof · cited by 2
- SimplexCategory.isIso_iff_of_monoproof · cited by 1
- SimplexCategory.eq_σ_of_epiproof · cited by 0