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Theorems · Definition · category theory

CategoryTheory.AddMon.trivial

(C : Type u₁) →
  [inst : CategoryTheory.Category.{v₁, u₁} C] → [inst_1 : CategoryTheory.MonoidalCategory C] → CategoryTheory.AddMon C

The trivial additive monoid object. We later show this is initial in AddMon C

Defined in
Mathlib.CategoryTheory.Monoidal.Mon
Cited by
11 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategory

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon · cited by 15EquivLaxMonoidalFunctorPU…CategoryTheory.AddGrp.trivial · cited by 5AddGrp.trivialCategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_functor_map_hom · cited by 0AddMon.equivLaxMonoidalFu…CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_functor_obj_addMon_add · cited by 0AddMon.equivLaxMonoidalFu…CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_functor_obj_addMon_zero · cited by 0AddMon.equivLaxMonoidalFu…CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon_map · cited by 0EquivLaxMonoidalFunctorPU…CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon_obj · cited by 0EquivLaxMonoidalFunctorPU…CategoryTheory.AddMon.trivial_X · cited by 0AddMon.trivial_XCategoryTheory.AddMon.trivial_addMon_add · cited by 0AddMon.trivial_addMon_addCategoryTheory.AddMon.isZero_trivial · cited by 0AddMon.isZero_trivialCategoryTheory.AddMon.trivial_addMon_zero · cited by 0AddMon.trivial_addMon_zeroCategoryTheory.AddMon.uniqueHomFromTrivial_default_hom · cited by 0AddMon.uniqueHomFromTrivi…CategoryTheory.AddMon.uniqueHomToTrivial_default_hom · cited by 0AddMon.uniqueHomToTrivial…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategoryStruct.tensorUnit · cited by 1384MonoidalCategoryStruct.te…CategoryTheory.AddMon · cited by 177CategoryTheory.AddMonAddMon.trivialCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by13

Results whose statement or proof uses this declaration.