Theorems · Definition · category theory
CategoryTheory.Limits.HasColimits
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropC has all (small) colimits if it has colimits of every shape that is as big as its hom-sets.
- Defined in
- Mathlib.CategoryTheory.Limits.HasLimits
- Cited by
- 139 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 3 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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.Limits.HasColimitsOfSizeproof · cited by 124
Cited by186
Results whose statement or proof uses this declaration.
- TopCat.Presheaf.stalkstatement and proof · cited by 407
- TopCat.Presheaf.germstatement and proof · cited by 208
- TopCat.Presheaf.stalkSpecializesstatement and proof · cited by 51
- AlgebraicGeometry.PresheafedSpace.Hom.stalkMapstatement and proof · cited by 40
- TopCat.Presheaf.stalkFunctorstatement and proof · cited by 37
- TopCat.Presheaf.stalkCongrstatement and proof · cited by 23
- TopCat.Presheaf.germ_resstatement and proof · cited by 19
- TopCat.Presheaf.pullbackstatement and proof · cited by 19
- TopCat.Presheaf.exists_germ_eqstatement and proof · cited by 14
- TopCat.Presheaf.stalk_hom_extstatement and proof · cited by 14
- TopCat.Presheaf.germ_res_applystatement and proof · cited by 14
- TopCat.Presheaf.Γgermstatement and proof · cited by 13