Theorems · Definition · category theory
CategoryTheory.Limits.IsColimit.desc
{J : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} J] →
{C : Type u₃} →
[inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
{F : CategoryTheory.Functor J C} →
{t : CategoryTheory.Limits.Cocone F} →
CategoryTheory.Limits.IsColimit t → (s : CategoryTheory.Limits.Cocone F) → t.pt ⟶ s.ptt.pt maps to all other cocone covertices
- Defined in
- Mathlib.CategoryTheory.Limits.IsLimit
- Cited by
- 144 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 11 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
- CategoryTheory.Limits.IsColimitstatement and proof · cited by 773
- CategoryTheory.Limits.Coconestatement and proof · cited by 746
Cited by263
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsInitial.toproof · cited by 119
- CategoryTheory.Limits.IsColimit.facstatement · cited by 82
- CategoryTheory.Limits.colimit.descproof · cited by 63
- CategoryTheory.Limits.IsColimit.hom_extproof · cited by 58
- CategoryTheory.Limits.cokernel.descproof · cited by 53
- CategoryTheory.Limits.biproduct.descproof · cited by 29
- CategoryTheory.ShortComplex.exact_of_g_is_cokernelproof · cited by 25
- CategoryTheory.Limits.Cofan.IsColimit.descproof · cited by 24
- CategoryTheory.ShortComplex.RightHomologyData.mapproof · cited by 23
- CategoryTheory.Limits.IsColimit.descCoconeMorphismproof · cited by 17
- CategoryTheory.Limits.IsColimit.mapproof · cited by 17
- CategoryTheory.Limits.IsColimit.opproof · cited by 14
Showing the 200 most cited of 263.