Theorems · Theorem · category theory

CategoryTheory.isSubterminal_of_isIso_diag

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {A : C}
  [inst_1 : CategoryTheory.Limits.HasBinaryProduct A A] [CategoryTheory.IsIso (CategoryTheory.Limits.diag A)],
  CategoryTheory.IsSubterminal A

If the diagonal morphism of A is an isomorphism, then it is subterminal. The converse of isSubterminal.isIso_diag.

Defined in

Mathlib.CategoryTheory.Subterminal

Cited by

0 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProductCategoryTheory.IsIso