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Theorems · Definition · category theory

CategoryTheory.FinCategory.equivAsType

(α : Type u_1) →
  [inst : Fintype α] →
    [inst_1 : CategoryTheory.SmallCategory α] →
      [inst_2 : CategoryTheory.FinCategory α] → CategoryTheory.FinCategory.AsType α ≌ α

The constructed category (AsType α) is indeed equivalent to α.

Defined in
Mathlib.CategoryTheory.FinCategory.AsType
Cited by
5 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeCategoryTheory.SmallCategoryCategoryTheory.FinCategory
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Around this declaration

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

CategoryTheory.Limits.hasFiniteLimits_of_hasLimitsOfSize · cited by 1Limits.hasFiniteLimits_of…CategoryTheory.Limits.ReflectsLimitsOfSize.reflectsFiniteLimits · cited by 0ReflectsLimitsOfSize.refl…CategoryTheory.Limits.PreservesLimitsOfSize.preservesFiniteLimits · cited by 0PreservesLimitsOfSize.pre…CategoryTheory.Limits.hasFiniteColimits_of_hasColimitsOfSize · cited by 0Limits.hasFiniteColimits_…CategoryTheory.Limits.PreservesColimitsOfSize.preservesFiniteColimits · cited by 0PreservesColimitsOfSize.p…Fintype · cited by 7736FintypeCategoryTheory.Equivalence · cited by 601CategoryTheory.EquivalenceCategoryTheory.SmallCategory · cited by 480CategoryTheory.SmallCateg…CategoryTheory.FinCategory · cited by 107CategoryTheory.FinCategoryCategoryTheory.Equivalence.trans · cited by 57Equivalence.transCategoryTheory.FinCategory.AsType · cited by 8FinCategory.AsTypeCategoryTheory.FinCategory.objAsTypeEquiv · cited by 0FinCategory.objAsTypeEquivCategoryTheory.FinCategory.asTypeEquivObjAsType · cited by 0FinCategory.asTypeEquivOb…FinCategory.equivAsTypeCITED BYCITES

Cites8

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Cited by5

Results whose statement or proof uses this declaration.