Theorems · Definition · category theory

CategoryTheory.Limits.mulIsInitial

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.Limits.HasStrictInitialObjects C] →
      {I : C} →
        (X : C) →
          [inst_2 : CategoryTheory.Limits.HasBinaryProduct X I] → CategoryTheory.Limits.IsInitial I → (X ⨯ I ≅ I)

If I is initial, then X ⨯ I is isomorphic to it.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.StrictInitial

Cited by

2 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasStrictInitialObjectsCategoryTheory.Limits.HasBinaryProduct