---- > [!definition] Definition. ([[groupoid]]) > A **groupoid** is a [[category]] in which every morphism is an [[isomorphism]]. Unlike a [[group]], a groupoid is permitted to have multiple objects (a group is a groupoid with a single object), meaning in particular that morphisms cannot be composed arbitrarily; they must type-check. In this sense, a groupoid can be viewed as a [[group]] $G$ whose [[binary operation]] is replaced with a [[partial function]] from $S \subset G \times G \to G$. ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```