Theorems · Theorem · category theory
CategoryTheory.MonObj.comp_one
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{M X Y : C} [inst_2 : CategoryTheory.MonObj M] (f : X ⟶ Y), CategoryTheory.CategoryStruct.comp f 1 = 1- Cited by
- 7 results in Mathlib
- Foundations
- Depth 44 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.MonObjstatement and proof · cited by 199
- CategoryTheory.Hom.monoidstatement · cited by 52
- MonCat.Hom.homproof · cited by 38
- MonoidHom.map_oneproof · cited by 27
- CategoryTheory.yonedaMonproof · cited by 10
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.GrpObj.η_whiskerRight_commutatorproof · cited by 2
- CategoryTheory.isCommMonObj_iff_commutator_eq_toUnit_ηproof · cited by 2
- CategoryTheory.GrpObj.whiskerLeft_η_commutatorproof · cited by 2
- CategoryTheory.MonObj.comp_powproof · cited by 2
- AlgebraicGeometry.isCommMonObj_of_isProper_of_geometricallyIntegralproof · cited by 0
- CategoryTheory.IsMonHom.Normal.of_isPullback_ηproof · cited by 0
- CategoryTheory.MonObj.comp_one_assocproof · cited by 0