CatDat

Implication Details

Assumptions: groupoid, multi-terminal object

Conclusions: thin

Proof: Let $f,g : A \rightrightarrows B$ be a parallel pair of morphisms. Since the category has a multi-terminal object, the connected component containing $A$ and $B$ has a terminal object. But since the category is a groupoid, both $A$ and $B$ are terminal objects in the connected component, hence $f=g$.