Theorems · Theorem · category theory
CategoryTheory.Groupoid.isThin_iff
∀ (C : Type u_1) [inst : CategoryTheory.Groupoid C], Quiver.IsThin C ↔ ∀ (c : C), Subsingleton (c ⟶ c)
- Defined in
- Mathlib.CategoryTheory.Groupoid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Groupoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.invproof · cited by 467
- CategoryTheory.CategoryStructproof · cited by 343
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.IsIso.inv_hom_idproof · cited by 88
- Quiver.IsThinstatement and proof · cited by 51
- CategoryTheory.Groupoid.invproof · cited by 36
- CategoryTheory.IsIso.hom_inv_id_assocproof · cited by 29
- CategoryTheory.Groupoid.inv_eq_invproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Subgroupoid.isThin_iffproof · cited by 0