Theorems · Theorem · category theory
SimplexCategory.isIso_iff_of_mono
∀ {n m : SimplexCategory} (f : n ⟶ m) [hf : CategoryTheory.Mono f], CategoryTheory.IsIso f ↔ n.len = m.len- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 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.
Cites10
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.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- SimplexCategory.lenstatement and proof · cited by 542
- Finite.injective_iff_surjectiveproof · cited by 9
- SimplexCategory.extproof · cited by 6
- SimplexCategory.mono_iff_injectiveproof · cited by 6
- SimplexCategory.len_eq_of_isIsoproof · cited by 3
- SimplexCategory.isIso_of_bijectiveproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- SimplexCategory.eq_id_of_monoproof · cited by 7