Theorems · Theorem · category theory
CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_id
∀ {Ω : Type w} {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (h : CategoryTheory.CoreSmallCategoryOfSet Ω C)
(X : ↑h.obj), h.smallCategoryOfSet.id X = h.homEquiv.symm (CategoryTheory.CategoryStruct.id (h.objEquiv X))- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- Equivstatement · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- Equiv.symmstatement · cited by 3,681
- CategoryTheory.CoreSmallCategoryOfSetstatement and proof · cited by 11
- CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSetstatement and proof · cited by 8
- CategoryTheory.CoreSmallCategoryOfSet.objstatement and proof · cited by 6
- CategoryTheory.CoreSmallCategoryOfSet.homstatement · cited by 4
- CategoryTheory.CoreSmallCategoryOfSet.objEquivstatement · cited by 4
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