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Theorems · Theorem · category theory

CategoryTheory.IsSifted.nonempty_of_colim_preservesLimitsOfShapeFinZero

∀ (C : Type u) [inst : CategoryTheory.SmallCategory C]
  [CategoryTheory.Limits.PreservesLimitsOfShape (CategoryTheory.Discrete (Fin 0)) CategoryTheory.Limits.colim],
  Nonempty C
Defined in
Mathlib.CategoryTheory.Limits.Sifted
Cited by
1 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.SmallCategoryCategoryTheory.Limits.PreservesLimitsOfShape
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.IsSifted.of_colim_preservesFiniteProducts · cited by 1IsSifted.of_colim_preserv…CategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.Cone.pt · cited by 1298Cone.ptCategoryTheory.Iso.refl · cited by 727Iso.reflCategoryTheory.Iso.trans · cited by 566Iso.transCategoryTheory.SmallCategory · cited by 480CategoryTheory.SmallCateg…CategoryTheory.evaluation · cited by 173CategoryTheory.evaluationCategoryTheory.Limits.PreservesLimitsOfShape · cited by 156Limits.PreservesLimitsOfS…CategoryTheory.Functor.mapCone · cited by 147Functor.mapConeCategoryTheory.Limits.colim · cited by 89Limits.colimCategoryTheory.Limits.HasColimit.isoOfNatIso · cited by 56HasColimit.isoOfNatIsoCategoryTheory.IsConnected · cited by 51CategoryTheory.IsConnectedCategoryTheory.Limits.terminalIsTerminal · cited by 31Limits.terminalIsTerminalCategoryTheory.Limits.Types.isTerminalPUnit · cited by 12Types.isTerminalPUnitIsSifted.nonempty_of_colim_pr…CITED BYCITES

Cites23

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Cited by1

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