Theorems · Definition · category theory
CategoryTheory.MonObj.one
{C : Type u₁} →
{inst : CategoryTheory.Category.{v₁, u₁} C} →
{inst_1 : CategoryTheory.MonoidalCategory C} →
{X : C} → [self : CategoryTheory.MonObj X] → CategoryTheory.MonoidalCategoryStruct.tensorUnit C ⟶ XThe unit morphism of a monoid object.
- Defined in
- Mathlib.CategoryTheory.Monoidal.Mon
- Cited by
- 189 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 12 definitions · uses no axioms
- Assumes
- CategoryTheory.MonObj
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 32,603
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
- CategoryTheory.MonObjstatement and proof · cited by 199
Cited by230
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.monObjObjproof · cited by 10
- CategoryTheory.MonObj.mul_onestatement · cited by 10
- CategoryTheory.MonObj.one_mulstatement · cited by 10
- CategoryTheory.Mon.Hom.mk'statement and proof · cited by 10
- CategoryTheory.HopfObj.antipode_leftstatement · cited by 6
- CategoryTheory.GrpObj.left_invstatement · cited by 6
- CategoryTheory.GrpObj.lift_comp_inv_leftstatement and proof · cited by 6
- CategoryTheory.GrpObj.lift_comp_inv_rightstatement and proof · cited by 6
- CategoryTheory.IsMonHom.one_homstatement · cited by 5
- CategoryTheory.MonObj.lift_comp_one_rightstatement and proof · cited by 5
- CategoryTheory.MonObj.one_eq_onestatement and proof · cited by 5
- CategoryTheory.Monad.ofMonproof · cited by 5
Showing the 200 most cited of 230.