Theorems · Theorem · category theory

AddCommGrpCat.hasColimit_iff_small_quot

∀ {J : Type u} [inst : CategoryTheory.Category.{v, u} J] {F : CategoryTheory.Functor J AddCommGrpCat}
  [inst_1 : DecidableEq J], CategoryTheory.Limits.HasColimit F ↔ Small.{w, max u w} (AddCommGrpCat.Colimits.Quot F)

A functor F : J ⥤ AddCommGrpCat.{w} has a colimit if and only if Colimits.Quot F is w-small.

Defined in

Mathlib.Algebra.Category.Grp.LargeColimits

Cited by

0 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryDecidableEq