Theorems · Definition · category theory
CategoryTheory.Functor.mapGrpIdIso
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
(CategoryTheory.Functor.id C).mapGrp ≅ CategoryTheory.Functor.id (CategoryTheory.Grp C)The identity functor is also the identity on group objects.
- Defined in
- Mathlib.CategoryTheory.Monoidal.Grp
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 40 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.
- 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.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.Grpstatement and proof · cited by 144
- CategoryTheory.Grp.Xproof · cited by 99
- CategoryTheory.Functor.mapGrpstatement and proof · cited by 32
- CategoryTheory.Grp.mkIsoproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.Equivalence.mapGrpproof · cited by 4
- CategoryTheory.Adjunction.mapGrpproof · cited by 2
- CategoryTheory.Functor.mapGrpIdIso_hom_app_hom_homstatement and proof · cited by 0
- CategoryTheory.Functor.mapGrpIdIso_inv_app_hom_homstatement and proof · cited by 0
- CategoryTheory.Equivalence.mapGrp_counitIsostatement · cited by 0
- CategoryTheory.Equivalence.mapGrp_unitIsostatement · cited by 0
- CategoryTheory.Adjunction.mapGrp_counitstatement · cited by 0
- CategoryTheory.Adjunction.mapGrp_unitstatement · cited by 0