Theorems · Definition · category theory
CategoryTheory.Mon.trivial
(C : Type u₁) →
[inst : CategoryTheory.Category.{v₁, u₁} C] → [inst_1 : CategoryTheory.MonoidalCategory C] → CategoryTheory.Mon CThe trivial monoid object. We later show this is initial in Mon C.
- Defined in
- Mathlib.CategoryTheory.Monoidal.Mon
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategoryStruct.tensorUnitproof · cited by 1,384
- CategoryTheory.Monstatement · cited by 465
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMonproof · cited by 15
- CategoryTheory.Grp.trivialproof · cited by 5
- CategoryTheory.Mon.uniqueHomToTrivial_default_homstatement · cited by 0
- CategoryTheory.Mon.uniqueHomFromTrivial_default_homstatement · cited by 0
- CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_mapstatement · cited by 0
- CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_objstatement · cited by 0
- CategoryTheory.uniqueHomToTrivialstatement · cited by 0
- CategoryTheory.Bimon.trivialTo_homstatement · cited by 0
- CategoryTheory.Mon.isZero_trivialstatement and proof · cited by 0
- CategoryTheory.Mon.trivial_mon_mulstatement · cited by 0
- CategoryTheory.Mon.trivial_Xstatement and proof · cited by 0
- CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_functor_map_homstatement · cited by 0