Theorems · Definition · category theory
Condensed.fintypeCatAsCofanIsColimit
(X : Profinite) → [Finite ↑X.toTop] → CategoryTheory.Limits.IsColimit (Condensed.fintypeCatAsCofan X)
A finite set is the coproduct of its points in Profinite.
- Defined in
- Mathlib.Condensed.Discrete.Colimit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- Finitestatement and proof · cited by 3,029
- CategoryTheory.Discretestatement · cited by 2,447
- TopCatstatement · cited by 1,889
- CategoryTheory.Limits.Cocone.ptproof · cited by 1,354
- CategoryTheory.Limits.IsColimitstatement · cited by 773
- CategoryTheory.Discrete.functorstatement · cited by 633
- TotallyDisconnectedSpacestatement · cited by 295
Cited by3
Results whose statement or proof uses this declaration.
- Condensed.isoFinYonedaComponentsproof · cited by 5
- Condensed.fintypeCatAsCofanIsColimit.congr_simpstatement and proof · cited by 0
- Condensed.isoFinYoneda_inv_app_hom_applystatement · cited by 0