Theorems · Inductive type · category theory
CategoryTheory.IsGroupoid
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA Prop-valued typeclass asserting that a given category is a groupoid.
- Defined in
- Mathlib.CategoryTheory.Groupoid
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.Bicategory.IsLocallyGroupoidproof · cited by 14
- CategoryTheory.isGroupoid_iff_isomorphisms_eq_topstatement and proof · cited by 1
- CategoryTheory.ObjectProperty.isDetecting_bot_of_isGroupoidstatement and proof · cited by 0
- CategoryTheory.ObjectProperty.isGroupoid_of_isCodetecting_botstatement · cited by 0
- CategoryTheory.ObjectProperty.isGroupoid_of_isDetecting_botstatement · cited by 0
- CategoryTheory.isGroupoid_of_reflects_isostatement and proof · cited by 0
- CategoryTheory.IsGroupoid.casesOnstatement and proof · cited by 0
- CategoryTheory.IsGroupoid.recOnstatement and proof · cited by 0
- CategoryTheory.Groupoid.ofIsGroupoidstatement and proof · cited by 0
- CategoryTheory.Localization.isGroupoidstatement · cited by 0
- CategoryTheory.ObjectProperty.isCodetecting_bot_of_isGroupoidstatement and proof · cited by 0