Theorems · Theorem · category theory
CategoryTheory.toSkeleton_eq_iff
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {Y : CategoryTheory.Skeleton C},
CategoryTheory.toSkeleton X = Y ↔ Nonempty (X ≅ (CategoryTheory.fromSkeleton C).obj Y)- Defined in
- Mathlib.CategoryTheory.Skeletal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Skeletonstatement and proof · cited by 35
- CategoryTheory.fromSkeletonstatement · cited by 10
- CategoryTheory.toSkeletonstatement · cited by 10
- Quotient.mk_eq_iff_outproof · cited by 4
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