Theorems · Definition · category theory
CategoryTheory.Codiscrete.equivFun
{X : Type u} →
{n : ℕ} → (CategoryTheory.nerve (CategoryTheory.Codiscrete X)).obj (Opposite.op { len := n }) ≃ (Fin (n + 1) → X)Since the morphisms in a codiscrete category do not carry information, an n-simplex of coherentIso is equivalent to an X-vector of length (n + 1).
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 62 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.
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Equivstatement · cited by 8,337
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.homproof · cited by 7,684
- Opposite.unopproof · cited by 2,231
- SimplexCategorystatement · cited by 2,204
- SimplexCategory.lenproof · cited by 542
- CategoryTheory.nervestatement and proof · cited by 68
- CategoryTheory.Codiscretestatement and proof · cited by 22
- CategoryTheory.Codiscrete.asproof · cited by 9
- CategoryTheory.Codiscrete.isoproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Codiscrete.equivFun_applystatement and proof · cited by 0
- CategoryTheory.Codiscrete.equivFun_symm_apply_mapstatement and proof · cited by 0
- CategoryTheory.Codiscrete.equivFun_symm_apply_obj_asstatement and proof · cited by 0