Definition 0.1
Groupoid categories, or
categories of groupoids, can be defined
simply by considering a
groupoid
as a
category

with all invertible
morphisms, and
objects
defined by the groupoid class or set of groupoid elements; then, the groupoid category,
,
is defined as the
-category whose objects are
categories (groupoids), and whose morphisms are
functors
of
categories consistent with the definition of
groupoid homomorphisms, or in the case of
topological groupoids, consistent as well with topological groupoid
homeomorphisms. The
2-category
of groupoids
, plays a central role in the generalised, categorical Galois theory involving
fundamental groupoid functors.