Theorems · Definition · category theory
SemiSimplexCategory.homEquiv
{n m : SemiSimplexCategory} → (n ⟶ m) ≃ (Fin (n.len + 1) ↪o Fin (m.len + 1))Morphisms n ⟶ m in SemiSimplexCategory identify to order embeddings
Fin (n.len + 1) ↪o Fin (m.len + 1).
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Equivstatement · cited by 8,337
- OrderEmbeddingstatement · cited by 619
- Equiv.reflproof · cited by 274
- SemiSimplexCategorystatement and proof · cited by 15
- SemiSimplexCategory.lenstatement · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- SemiSimplexCategory.toSimplexCategoryproof · cited by 4
- SemiSimplexCategory.homOfMonoproof · cited by 3
- SemiSimplexCategory.hom_extstatement and proof · cited by 1
- SemiSimplexCategory.homEquiv_compstatement · cited by 0
- SemiSimplexCategory.homEquiv_idstatement · cited by 0
- SemiSimplexCategory.hom_ext_iffstatement and proof · cited by 0