Theorems · Theorem · category theory
CategoryTheory.GrpObj.comp_inv
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{G X Y : C} [inst_2 : CategoryTheory.GrpObj G] (f : X ⟶ Y) (g : Y ⟶ G),
CategoryTheory.CategoryStruct.comp f g⁻¹ = (CategoryTheory.CategoryStruct.comp f g)⁻¹- Cited by
- 10 results in Mathlib
- Foundations
- Depth 47 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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Functor.mapproof · cited by 8,698
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.GrpObjstatement and proof · cited by 99
- GrpCat.Hom.homproof · cited by 47
- CategoryTheory.Hom.groupstatement · cited by 25
- MonoidHom.map_invproof · cited by 16
- CategoryTheory.yonedaGrpproof · cited by 9
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_invproof · cited by 2
- CategoryTheory.GrpObj.lift_conj_eq_mul_mul_invproof · cited by 2
- CategoryTheory.GrpObj.whiskerLeft_η_commutatorproof · cited by 2
- CategoryTheory.GrpObj.η_whiskerRight_commutatorproof · cited by 2
- CategoryTheory.GrpObj.one_invproof · cited by 1
- CategoryTheory.GrpObj.comp_zpowproof · cited by 1
- AlgebraicGeometry.isCommMonObj_of_isProper_of_geometricallyIntegralproof · cited by 0
- CategoryTheory.IsMonHom.normal_iff_normal_monoidHomproof · cited by 0
- CategoryTheory.GrpObj.comp_inv_assocproof · cited by 0
- CategoryTheory.IsMonHom.Normal.of_isPullback_ηproof · cited by 0