Theorems · Inductive type · category theory
CategoryTheory.SemiCartesianMonoidalCategory
(C : Type u) → [CategoryTheory.Category.{v, u} C] → Type (max u v)A monoidal category is semicartesian if the unit for the tensor product is a terminal object.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by33
Results whose statement or proof uses this declaration.
- CategoryTheory.SemiCartesianMonoidalCategory.fststatement and proof · cited by 184
- CategoryTheory.SemiCartesianMonoidalCategory.sndstatement and proof · cited by 181
- CategoryTheory.SemiCartesianMonoidalCategory.toUnitstatement and proof · cited by 103
- CategoryTheory.SemiCartesianMonoidalCategory.isTerminalTensorUnitstatement and proof · cited by 30
- CategoryTheory.SemiCartesianMonoidalCategory.toUnit_uniquestatement and proof · cited by 26
- CategoryTheory.SemiCartesianMonoidalCategory.fst_defstatement and proof · cited by 13
- CategoryTheory.SemiCartesianMonoidalCategory.snd_defstatement and proof · cited by 10
- CategoryTheory.SemiCartesianMonoidalCategory.comp_toUnit_assocstatement and proof · cited by 5
- CategoryTheory.SemiCartesianMonoidalCategory.comp_toUnitstatement and proof · cited by 1
- CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unitstatement and proof · cited by 1
- CategoryTheory.AddMon.isZero_trivialstatement and proof · cited by 0
- CategoryTheory.CartesianMonoidalCategory.mk.noConfusionstatement and proof · cited by 0