Vector Symbolic Architectures (VSAs) generally consist of a hyper-algebra that is defined on points in a space of vectors. However, such a space is typically defined in usual ways, such as Euclidean Spaces for real vectors, Hamming Spaces for binary vectors, and so on. In any empirical setting, such as Artificial Intelligence, Machine Learning, Data Science, etc., observations in these spaces tend to produce subspaces of these broader spaces. As a result, these empirically-derived subspaces enable VSAs to make predictions through how severely the subspaces deviate from what is expected. Thus, it is desirable to be able to understand how such subspaces behave. As an analogy, when one observes terrain, they should find good "roads and bridges" to navigate that terrain. In Category Theory, the idea of Topos describes how such roads and bridges should be placed. In this paper, we explore the relationship between VSAs and Topoi. Namely, we show how a Topos-like representation can be constructed from empirical observations of vectors and demonstrate this on a practical example using Hyperdimensional Computing (HDC) on dense binary hypervectors. Our results indicate that a Topos can be effectively constructed for a dataset and the resulting space of vectors is biased to reflect the compositional aspects of the data. We conclude that such a Topos can be used to better guide the construction of VSAs for downstream tasks, in lieu of the original space of vectors, much like manifolds in Topology.