Theorems · Theorem · category theory
CategoryTheory.Projective.projective_iff_preservesEpimorphisms_coyoneda_obj
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : C),
CategoryTheory.Projective P ↔ (CategoryTheory.coyoneda.obj (Opposite.op P)).PreservesEpimorphisms- Cited by
- 3 results in Mathlib
- Foundations
- Depth 28 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.
Cites14
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.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement · cited by 8,081
- Opposite.unopproof · cited by 2,231
- CategoryTheory.Epiproof · cited by 688
- CategoryTheory.coyonedastatement and proof · cited by 208
- CategoryTheory.Projectivestatement and proof · cited by 78
- CategoryTheory.Functor.PreservesEpimorphismsstatement and proof · cited by 41
- CategoryTheory.epi_iff_surjectiveproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.