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I am reading the paper Chern-Weil map for principal bundles over groupoids. In page number $13$, authors say let us recall the definition of fundamental group of a topological groupoid. But, they ...

Let $X,Y$ be two connected, non-singular compact Riemann surfaces such that $X$ intersects $Y$ transversely at two distinct points. Let $L$ be a $\mathbb{C}$-local system on $X$. Let $L'$ be the ...

(Note that I've edited the main body of the question to make it clear for other readers.) Fix a principal $G$-bundle $\rho: P \rightarrow X$ and fix a point $p \in P_x$ in the fiber above $x \in X$. ...