  The philosophy of the Loop Quantum Gravity approach is to construct the
canonical variables by using the duality of infinitesimal connections and
holonomies along loops. Based on this fundamental property for example the
holonomy-flux *-algebra has been formulated. A generalisation of the one-to-one
correspondence between infinitesimal objects: connections and curvature and
path based objects: holonomy maps and parallel transports is used to replace
the configuration space of the theory. This generalised duality is related to
the concept of path connections and holonomy groupoids, which originally has
been invented by Mackenzie and which is presented shortly in this article.
Finally these objects are used to propose some new algebras of quantum
variables for Loop Quantum Gravity.
