Mathlib Map

Theorems · Definition · category theory

CategoryTheory.SemiCartesianMonoidalCategory.isTerminalTensorUnit

{C : Type u} →
  {inst : CategoryTheory.Category.{v, u} C} →
    [self : CategoryTheory.SemiCartesianMonoidalCategory C] →
      CategoryTheory.Limits.IsTerminal (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)

The tensor unit is a terminal object.

Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
Cited by
30 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.SemiCartesianMonoidalCategory

Around this declaration

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

CategoryTheory.SemiCartesianMonoidalCategory.toUnit · cited by 103SemiCartesianMonoidalCate…CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fst · cited by 24CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.whiskerLeft_snd · cited by 19CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd · cited by 16CartesianMonoidalCategory…CategoryTheory.SemiCartesianMonoidalCategory.fst_def · cited by 13SemiCartesianMonoidalCate…CategoryTheory.CartesianMonoidalCategory.whiskerRight_fst · cited by 13CartesianMonoidalCategory…CategoryTheory.SemiCartesianMonoidalCategory.snd_def · cited by 10SemiCartesianMonoidalCate…CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso · cited by 8CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.associator_hom_fst · cited by 8CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_fst · cited by 7CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst · cited by 7CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd · cited by 7CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_snd · cited by 6CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.associator_inv_snd · cited by 6CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fst · cited by 6CartesianMonoidalCategory…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MonoidalCategoryStruct.tensorUnit · cited by 1384MonoidalCategoryStruct.te…CategoryTheory.Limits.IsTerminal · cited by 153Limits.IsTerminalCategoryTheory.SemiCartesianMonoidalCategory · cited by 14CategoryTheory.SemiCartes…SemiCartesianMonoidalCategory…CITED BYCITES

Cites4

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Cited by35

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