Theorems · Theorem · category theory
CategoryTheory.GrpObj.inv_comp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{G H X : C} [inst_2 : CategoryTheory.GrpObj G] [inst_3 : CategoryTheory.GrpObj H] (f : X ⟶ G) (g : G ⟶ H)
[CategoryTheory.IsMonHom g], CategoryTheory.CategoryStruct.comp f⁻¹ g = (CategoryTheory.CategoryStruct.comp f g)⁻¹- Cited by
- 2 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Category.assocproof · cited by 6,433
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.GrpObjstatement and proof · cited by 99
- CategoryTheory.IsMonHomstatement and proof · cited by 56
- CategoryTheory.GrpObj.invproof · cited by 50
- CategoryTheory.Hom.groupstatement · cited by 25
- CategoryTheory.GrpObj.inv_homproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.IsMonHom.Normal.of_isPullback_ηproof · cited by 0
- CategoryTheory.GrpObj.inv_comp_assocproof · cited by 0