Theorems · Inductive type · category theory

CategoryTheory.EffectiveEpi

{C : Type u_1} → [inst : CategoryTheory.Category.{v_1, u_1} C] → {X Y : C} → (Y ⟶ X) → Prop

A morphism f : Y ⟶ X is an effective epimorphism provided that f exhibits X as a colimit of the diagram of all "relations" R ⇉ Y. If f has a kernel pair, then this is equivalent to showing that the corresponding cofork is a colimit.

Defined in

Mathlib.CategoryTheory.EffectiveEpi.Basic

Cited by

86 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.Category