Theorems · Definition · category theory

CategoryTheory.FinCategory.asTypeEquivObjAsType

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

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

Defined in: Mathlib.CategoryTheory.FinCategory.AsType
Cited by: 0 results in Mathlib
Foundations: Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype CategoryTheory.SmallCategory CategoryTheory.FinCategory

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Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
Equivstatement · cited by 8,337
Fintypestatement and proof · cited by 7,736
Equiv.symmstatement · cited by 3,681
Fintype.cardstatement · cited by 1,386
CategoryTheory.Iso.reflproof · cited by 727
CategoryTheory.Equivalencestatement · cited by 601
CategoryTheory.SmallCategorystatement and proof · cited by 480
CategoryTheory.NatIso.ofComponentsproof · cited by 178
CategoryTheory.FinCategorystatement and proof · cited by 107
Fintype.equivFinstatement · cited by 51
CategoryTheory.FinCategory.AsTypestatement · cited by 8

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.FinCategory.equivAsTypeproof · cited by 5