Theorems · Definition · category theory
CategoryTheory.Functor.mapCommMonIdIso
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.MonoidalCategory C] →
[inst_2 : CategoryTheory.BraidedCategory C] →
(CategoryTheory.Functor.id C).mapCommMon ≅ CategoryTheory.Functor.id (CategoryTheory.CommMon C)The identity functor is also the identity on commutative monoid objects.
- Defined in
- Mathlib.CategoryTheory.Monoidal.CommMon_
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Functor.idstatement and proof · cited by 3,333
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.BraidedCategorystatement and proof · cited by 779
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.CommMonstatement and proof · cited by 85
- CategoryTheory.CommMon.Xproof · cited by 50
- CategoryTheory.Functor.mapCommMonstatement and proof · cited by 27
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.Equivalence.mapCommMonproof · cited by 4
- CategoryTheory.Adjunction.mapCommMonproof · cited by 2
- CategoryTheory.Functor.mapCommMonIdIso_hom_app_hom_homstatement and proof · cited by 0
- CategoryTheory.Functor.mapCommMonIdIso_inv_app_hom_homstatement and proof · cited by 0
- CategoryTheory.Equivalence.mapCommMon_counitIsostatement · cited by 0
- CategoryTheory.Equivalence.mapCommMon_unitIsostatement · cited by 0
- CategoryTheory.Adjunction.mapCommMon_counitstatement · cited by 0
- CategoryTheory.Adjunction.mapCommMon_unitstatement · cited by 0