Theorems · Theorem · category theory

CategoryTheory.Limits.InitialMonoClass.of_terminal

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Limits.HasInitial C]
  [inst_2 : CategoryTheory.Limits.HasTerminal C],
  CategoryTheory.Mono (CategoryTheory.Limits.initial.to (⊤_ C)) → CategoryTheory.Limits.InitialMonoClass C

To show a category is an InitialMonoClass it suffices to show the unique morphism from the initial object to a terminal object is a monomorphism.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Terminal

Cited by

0 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasInitialCategoryTheory.Limits.HasTerminal