  An important goal is to understand better the relation between full loop
quantum gravity (LQG) and the simplified, reduced theory known as loop quantum
cosmology (LQC), {\em directly at the quantum level}. Such a firmer
understanding would increase confidence in the reduced theory as a tool for
formulating predictions of the full theory, as well as permitting lessons from
the reduced theory to guide further development in the full theory. The present
paper constructs an embedding of the usual state space of LQC into that of
standard LQG, that is, LQG based on \textit{piecewise analytic paths}. The
embedding is well-defined even prior to solving the diffeomorphism constraint,
at no point is a graph fixed, and at no point is the piecewise linear category
used. This motivates for the first time a definition of operators in LQC
corresponding to holonomies along non-piecewise-linear paths, without changing
the usual kinematics of LQC in any way. The new embedding intertwines all
operators corresponding to such holonomies, and all elements in its image
satisfy an operator equation which classically implies homogeneity and
isotropy. The construction is made possible by a recent result proven by
Fleischhack.
