Theorems · Definition · category theory
CategoryTheory.Functor.mapGrpNatIso
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
{D : Type u₂} →
[inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
[inst_3 : CategoryTheory.CartesianMonoidalCategory D] →
{F F' : CategoryTheory.Functor C D} →
[inst_4 : F.Monoidal] → [inst_5 : F'.Monoidal] → (F ≅ F') → (F.mapGrp ≅ F'.mapGrp)Natural isomorphisms between functors lift to group objects.
- Defined in
- Mathlib.CategoryTheory.Monoidal.Grp
- Cited by
- 4 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.
Cites11
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.Functorstatement and proof · cited by 16,252
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.Functor.Monoidalstatement and proof · cited by 288
- CategoryTheory.Iso.appproof · cited by 253
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.Grpstatement and proof · cited by 144
- CategoryTheory.Grp.Xproof · cited by 99
- CategoryTheory.Functor.mapGrpstatement · cited by 32
- CategoryTheory.Grp.mkIsoproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Equivalence.mapGrpproof · cited by 4
- CategoryTheory.Functor.mapGrpNatIso_hom_app_hom_homstatement and proof · cited by 0
- CategoryTheory.Functor.mapGrpNatIso_inv_app_hom_homstatement and proof · cited by 0
- CategoryTheory.Equivalence.mapGrp_counitIsostatement · cited by 0
- CategoryTheory.Equivalence.mapGrp_unitIsostatement · cited by 0