Theorems · Theorem · category theory

CategoryTheory.Functor.EffectivelyEnough.presentation

∀ {C : Type u_1} {D : Type u_2} {inst : CategoryTheory.Category.{v_1, u_1} C}
  {inst_1 : CategoryTheory.Category.{v_2, u_2} D} {F : CategoryTheory.Functor C D} [self : F.EffectivelyEnough] (X : D),
  Nonempty (F.EffectivePresentation X)

For every X : D, there exists an object p of C with an effective epi F.obj p ⟶ X.

Defined in: Mathlib.CategoryTheory.EffectiveEpi.Enough
Cited by: 4 results in Mathlib
Foundations: Depth 3 from the axioms · uses no axioms
Assumes: CategoryTheory.Functor.EffectivelyEnough

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Cites4

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
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.EffectivelyEnoughstatement and proof · cited by 9
CategoryTheory.Functor.EffectivePresentationstatement · cited by 5

Cited by6

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.effectiveEpiOverproof · cited by 4
CategoryTheory.Functor.reflects_precoherentproof · cited by 3
CategoryTheory.Functor.reflects_preregularproof · cited by 3
CategoryTheory.coherentTopology.exists_effectiveEpiFamily_iff_mem_inducedproof · cited by 1
CategoryTheory.regularTopology.exists_effectiveEpi_iff_mem_inducedproof · cited by 1
CategoryTheory.Functor.effectiveEpiOverObjproof · cited by 1