Theorems · Theorem · category theory
CategoryTheory.GrpObj.inv_hom
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{A B : C} [inst_2 : CategoryTheory.GrpObj A] [inst_3 : CategoryTheory.GrpObj B] (f : A ⟶ B)
[CategoryTheory.IsMonHom f],
CategoryTheory.CategoryStruct.comp CategoryTheory.GrpObj.inv f =
CategoryTheory.CategoryStruct.comp f CategoryTheory.GrpObj.invMorphisms of group objects preserve inverses.
- Defined in
- Mathlib.CategoryTheory.Monoidal.Grp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.MonoidalCategoryStruct.tensorObjproof · cited by 3,106
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.MonoidalCategoryStruct.whiskerLeftproof · cited by 915
- CategoryTheory.MonoidalCategoryStruct.whiskerRightproof · cited by 903
- CategoryTheory.MonoidalCategoryStruct.associatorproof · cited by 667
- CategoryTheory.MonObj.mulproof · cited by 230
- CategoryTheory.MonObj.oneproof · cited by 189
- CategoryTheory.SemiCartesianMonoidalCategory.fstproof · cited by 184
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.GrpObj.inv_compproof · cited by 2
- CategoryTheory.GrpObj.inv_hom_assocproof · cited by 0