Theorems · Definition · category theory
CategoryTheory.Limits.Cofan.IsColimit.desc
{β : Type w} →
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{F : β → C} →
{c : CategoryTheory.Limits.Cofan F} →
CategoryTheory.Limits.IsColimit c → {A : C} → ((i : β) → F i ⟶ A) → (c.pt ⟶ A)Constructor for morphisms from the point of a colimit cofan.
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 32,603
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
- CategoryTheory.Limits.IsColimitstatement and proof · cited by 773
- CategoryTheory.Discrete.functorstatement · cited by 633
- CategoryTheory.Limits.IsColimit.descproof · cited by 144
- CategoryTheory.Limits.Cofanstatement and proof · cited by 124
- CategoryTheory.Limits.Cofan.mkproof · cited by 105
Cited by43
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimitproof · cited by 29
- CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimitproof · cited by 29
- SheafOfModules.freeHomEquivproof · cited by 20
- CategoryTheory.Limits.Cofan.IsColimit.facstatement · cited by 17
- CategoryTheory.SimplicialObject.Splitting.descproof · cited by 12
- CategoryTheory.PreZeroHypercover.sigmaOfIsColimitproof · cited by 9
- CategoryTheory.PreOneHypercover.sigmaOfIsColimitproof · cited by 6
- CategoryTheory.Limits.Multicofork.toSigmaCoforkproof · cited by 5
- CategoryTheory.Limits.MonoCoprod.binaryCofanSumproof · cited by 4
- CategoryTheory.Limits.MonoCoprod.isColimitBinaryCofanSumproof · cited by 4
- CategoryTheory.GradedObject.mapBifunctor₁₂BifunctorDescproof · cited by 3
- CategoryTheory.GradedObject.mapBifunctorBifunctor₂₃Descproof · cited by 3