Theorems · Definition · category theory

CategoryTheory.MonoOver

{C : Type u₁} → [CategoryTheory.Category.{v₁, u₁} C] → C → Type (max u₁ v₁)

The category of monomorphisms into X as a full subcategory of the over category. This isn't skeletal, so it's not a partial order. Later we define Subobject X as the quotient of this by isomorphisms.

Defined in

Mathlib.CategoryTheory.Subobject.MonoOver

Cited by

115 results in Mathlib

Foundations

Depth 28 from the axioms, rests on 140 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category