Theorems · Definition · category theory
AddCommGrpCat.Colimits.Quot
{J : Type u} →
[inst : CategoryTheory.Category.{v, u} J] → CategoryTheory.Functor J AddCommGrpCat → [DecidableEq J] → Type (max u w)The candidate for the colimit of F, defined as the quotient of the direct sum
of the commutative groups F.obj j by the relations given by the morphisms in
the diagram.
- Defined in
- Mathlib.Algebra.Category.Grp.Colimits
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- HasQuotient.Quotientproof · cited by 2,301
- DFinsuppproof · cited by 694
- AddCommGrpCatstatement and proof · cited by 462
- AddCommGrpCat.carrierproof · cited by 407
- AddCommGrpCat.Colimits.Relationsproof · cited by 5
Cited by25
Results whose statement or proof uses this declaration.
- AddCommGrpCat.Colimits.Quot.ιstatement · cited by 9
- AddCommGrpCat.Colimits.Quot.descstatement · cited by 7
- AddCommGrpCat.Colimits.toCoconestatement and proof · cited by 4
- AddCommGrpCat.Colimits.Quot.addMonoidHom_extstatement and proof · cited by 4
- AddCommGrpCat.Colimits.Quot.ι_descstatement · cited by 4
- AddCommGrpCat.Colimits.colimitCoconestatement and proof · cited by 4
- AddCommGrpCat.isColimit_iff_bijective_descstatement and proof · cited by 1
- AddCommGrpCat.hasColimit_of_small_quotstatement and proof · cited by 1
- AddCommGrpCat.Colimits.Quot.desc_toCocone_descstatement and proof · cited by 1
- AddCommGrpCat.Colimits.Quot.map_ιstatement · cited by 1
- AddCommGrpCat.Colimits.colimitCoconeIsColimitstatement and proof · cited by 1
- AddCommGrpCat.Colimits.isColimit_of_bijective_descstatement · cited by 1