Theorems · Definition · category theory

CategoryTheory.equivPUnit

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      [CategoryTheory.MonoidalClosed C] →
        [CategoryTheory.Limits.HasZeroObject C] → C ≌ CategoryTheory.Discrete PUnit.{w + 1}

A Cartesian closed category with a zero object is equivalent to the category with one object and one morphism.

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Zero

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonoidalClosedCategoryTheory.Limits.HasZeroObject