Theorems · Theorem · category theory

CategoryTheory.Functor.regularEpiOfPreserves_W

∀ {C : Type u_3} {D : Type u_4} [inst : CategoryTheory.Category.{v_3, u_3} C]
  [inst_1 : CategoryTheory.Category.{v_4, u_4} D] {X Y : C} (f : X ⟶ Y) [inst_2 : CategoryTheory.EffectiveEpi f]
  (F : CategoryTheory.Functor C D) [inst_3 : F.PreservesEffectiveEpis]
  [inst_4 : CategoryTheory.Limits.PreservesLimitsOfShape CategoryTheory.Limits.WalkingCospan F]
  (c : CategoryTheory.Limits.PullbackCone f f) (hc : CategoryTheory.Limits.IsLimit c),
  (CategoryTheory.Functor.regularEpiOfPreserves f F c hc).W = F.obj c.pt

Defined in: Mathlib.CategoryTheory.EffectiveEpi.Preserves
Cited by: 0 results in Mathlib
Foundations: Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.EffectiveEpi CategoryTheory.Functor.PreservesEffectiveEpis CategoryTheory.Limits.PreservesLimitsOfShape

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.mapstatement · cited by 8,698
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
CategoryTheory.Limits.WalkingCospanstatement and proof · cited by 496
CategoryTheory.Limits.cospanstatement · cited by 467
CategoryTheory.Limits.PreservesLimitsOfShapestatement and proof · cited by 156
CategoryTheory.Limits.PullbackConestatement and proof · cited by 136

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