Theorems · Definition · category theory

CategoryTheory.Limits.prodIsProd

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (X Y : C) →
      [inst_1 : CategoryTheory.Limits.HasBinaryProduct X Y] →
        CategoryTheory.Limits.IsLimit
          (CategoryTheory.Limits.BinaryFan.mk CategoryTheory.Limits.prod.fst CategoryTheory.Limits.prod.snd)

The binary fan constructed from the projection maps is a limit.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts

Cited by

7 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProduct