Theorems · Definition · category theory
CategoryTheory.IsFinitelyPresentable
{C : Type u} → [CategoryTheory.Category.{v, u} C] → C → PropAn object X is finitely presentable if Hom(X, -) preserves all filtered colimits.
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 104 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.
Cites3
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
- Cardinal.aleph0proof · cited by 521
- CategoryTheory.IsCardinalPresentableproof · cited by 39
Cited by18
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.ColimitPresentation.bindstatement and proof · cited by 5
- CategoryTheory.ObjectProperty.isFinitelyPresentableproof · cited by 4
- CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimitstatement and proof · cited by 3
- CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit_understatement and proof · cited by 2
- CategoryTheory.isFinitelyPresentable_iff_preservesFilteredColimitsstatement · cited by 1
- CategoryTheory.ObjectProperty.ind_iff_existsstatement and proof · cited by 1
- CategoryTheory.ObjectProperty.ind_indproof · cited by 1
- CategoryTheory.Limits.ColimitPresentation.bind_diag_objstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.ind_iff_existsproof · cited by 1
- CommRingCat.isFinitelyPresentable_understatement · cited by 1
- CategoryTheory.Limits.ColimitPresentation.bind.congr_simpstatement and proof · cited by 0