  In this paper we propose and study few applications of the base structured
categories $\mathcal{X} \rtimes_{\mathbf{F}} \mathbf{C}$, $\int_{\mathbf{C}}
\bar{\mathbf{F}}$, $\mathcal{X} \rtimes_{\mathbb{F}} \mathbf{C}$ and
${\int_{\mathbf{C}} \bar{\mathbb{F}}}$. First we show classic transformation
groupoid $X /\!\!/ G$ simply being a base-structured category
${\int_{\mathbf{G}} \bar{{F}}}$. Then using permutation action on a finite set,
we introduce the notion of a hierarchy of base structured categories
$[(\mathcal{X}_{2a} \rtimes_{\mathbf{F_{2a}}} \mathbf{B}_{2a}) \amalg
(\mathcal{X}_{2b} \rtimes_{\mathbf{F_{2b}}} \mathbf{B}_{2b}) \amalg ...]
\rtimes_{\mathbf{F_{1}}} \mathbf{B}_1$ that models local and global structures
as a special case of composite Grothendieck fibration. Further utilizing the
existing notion of transformation double category $(\mathcal{X}_{1}
\rtimes_{\mathbf{F_{1}}} \mathbf{B}_{1}) /\!\!/ \mathbf{2G}$, we demonstrate
that a hierarchy of bases naturally leads one from 2-groups to n-category
theory. Finally we prove that every classic Klein geometry is the Grothendieck
completion ($\mathbf{G} = \mathcal{X} \rtimes_{\mathbb{F}} \mathbf{H}$) of
${\mathbb{F}}: \mathbf{H} \xrightarrow{{F}} \mathbf{Man}^{\infty}
\xrightarrow{U} \mathbf{Set}$. This is generalized to propose a set-theoretic
definition of a groupoid geometry $(\mathcal{G},\mathcal{B})$ (originally
conceived by Ehresmann through transport and later by Leyton using transfer)
with a principal groupoid $\mathcal{G} = \mathcal{X} \rtimes \mathcal{B}$ and
geometry space $\mathcal{X} = \mathcal{G}/\mathcal{B}$; which is essentially
same as $\mathbf{G} = \mathcal{X} \rtimes_{\mathbb{F}} \mathbf{B}$ or precisely
the completion of ${\mathbb{F}}: \mathbf{B} \xrightarrow{{F}}
\mathbf{Man}^{\infty} \xrightarrow{U} \mathbf{Set}$.
