Theorems · Definition · category theory

CategoryTheory.IsFiltered.coeq

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.IsFilteredOrEmpty C] → {j j' : C} → (j ⟶ j') → (j ⟶ j') → C

coeq f f', for morphisms f f' : j ⟶ j', is an arbitrary choice of object which admits a morphism coeqHom f f' : j' ⟶ coeq f f' such that coeq_condition : f ≫ coeqHom f f' = f' ≫ coeqHom f f'. Its existence is ensured by IsFiltered.

Defined in

Mathlib.CategoryTheory.Filtered.Basic

Cited by

18 results in Mathlib

Foundations

Depth 9 from the axioms · uses Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.IsFilteredOrEmpty