Theorems · Definition · category theory
CommRingCat.coyonedaUnique
{n : Type v} → [Unique n] → CommRingCat.coyoneda.obj (Opposite.op n) ≅ CategoryTheory.Functor.id CommRingCatIf n is a singleton, Hom(n, -) is the identity in CommRingCat.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Unique
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement · cited by 8,081
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Functor.idstatement · cited by 3,333
- CommRingCatstatement and proof · cited by 2,333
- Opposite.unopproof · cited by 2,231
- CommRingCat.carrierproof · cited by 1,096
- Uniquestatement and proof · cited by 400
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- RingEquiv.toCommRingCatIsoproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- CommRingCat.coyonedaUnique_hom_app_hom_applystatement and proof · cited by 0
- CommRingCat.coyonedaUnique_inv_app_hom_applystatement and proof · cited by 0