Theorems · Definition · category theory
CategoryTheory.Limits.Cofan.mk
{β : Type w} →
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{f : β → C} → (P : C) → ((b : β) → f b ⟶ P) → CategoryTheory.Limits.Cofan fA cofan over f : β → C consists of a collection of maps from every f b to an object P.
- Cited by
- 105 results in Mathlib
- Foundations
- Depth 23 from the axioms, rests on 126 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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 and proof · cited by 32,603
- CategoryTheory.Discreteproof · cited by 2,447
- CategoryTheory.Discrete.asproof · cited by 269
- CategoryTheory.Limits.Cofanstatement · cited by 124
- CategoryTheory.Discrete.natTransproof · cited by 57
Cited by152
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.Sigma.descproof · cited by 76
- CategoryTheory.SimplicialObject.Splitting.cofanproof · cited by 46
- CategoryTheory.Limits.coproductIsCoproductstatement · cited by 31
- CategoryTheory.Limits.biproduct.descproof · cited by 29
- CategoryTheory.Limits.Cofan.IsColimit.descproof · cited by 24
- CategoryTheory.Limits.biproduct.ι_descproof · cited by 20
- CategoryTheory.Limits.FormalCoproduct.cofanproof · cited by 20
- CategoryTheory.Limits.Cofan.IsColimit.facproof · cited by 17
- SSet.relativeCellComplexOfMonoproof · cited by 14
- CategoryTheory.Limits.Sigma.ι_comp_map'proof · cited by 14
- CategoryTheory.Limits.Sigma.ι_descproof · cited by 13
- HomotopicalAlgebra.AttachCells.reindexproof · cited by 9