Theorems · Inductive type · category theory
CategoryTheory.Projective
{C : Type u} → [CategoryTheory.Category.{v, u} C] → C → PropAn object P is called projective if every morphism out of P factors through every epimorphism.
- Cited by
- 78 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by99
Results whose statement or proof uses this declaration.
- CategoryTheory.Presheaf.coherentExtensiveEquivalencestatement and proof · cited by 11
- CategoryTheory.Projective.factorThrustatement and proof · cited by 9
- CategoryTheory.Projective.factorThru_compstatement and proof · cited by 8
- CategoryTheory.Projective.factorsstatement and proof · cited by 6
- CategoryTheory.ShortComplex.Exact.liftFromProjective_compstatement and proof · cited by 5
- CategoryTheory.Abelian.Ext.eq_zero_of_projectivestatement and proof · cited by 4
- CategoryTheory.ProjectiveResolution.selfstatement and proof · cited by 4
- CategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₃_iffstatement and proof · cited by 4
- CategoryTheory.ShortComplex.Exact.liftFromProjectivestatement and proof · cited by 3
- IsProjective.iff_projectivestatement and proof · cited by 3
- CategoryTheory.Presheaf.isSheaf_iff_preservesFiniteProducts_of_projectivestatement and proof · cited by 3
- CategoryTheory.Projective.projective_iff_preservesEpimorphisms_coyoneda_objstatement and proof · cited by 3