Consider the category $BiGraph$ of bipartite graphs (vertices are named "places" and "transitions" like in Petri nets) and continous maps. A subgraph is named open iff it is place-bordered, and a map is named continous iff it is continous with repect to the induced topologies.

Formally: Consider a bipartite graph with vertex set $X$ and adjacency relation $ad$, and an induced subgraph spanned by a vertex set $U \subset X$. Then the subgraph is open iff for all $p,t\in X:$

$$t \in U \ and \ (p,t) \in ad \implies p \in U.$$ (Transitions from $U$ are adjacent to places only in $U$)

My question: Does the category $BiGraph$ have products and coproducts?

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