[[Types of Category]]
# Groupoid
A **groupoid** is the [[Oidification]] of a [[group]].
Thus a groupoid is a [[category]] in which all morphisms are [[isomorphism|isomorphisms]]. #m/def/cat
As such, it is a category augmented with an operation on morphisms  $\inv$ 
(often written as $(-)^{-1}$) 
such that
$$
\begin{align*}
f \circ \inv{(f)} = \id = \inv{(f)} \circ f
\end{align*}
$$
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