I will introduce a new model of relational databases called ``simplicial databases." These form a category, in which morphisms are transformations of databases that preserve the integrity of the data. One can show that colimits and limits in this category correspond to queries such as union, join, and select.

More interestingly, the schemas of these databases have natural topological shapes, called simplicial sets. For example, a rudimentary schema for round-trip flights would be an oriented circle consisting of an arrow from A to B and an arrow from B back to A. Note, however, that this is not just a visualization; it is mathematical structure encoded into the definition of simplicial databases. One can thus use topological methods such as homology theory (which already exists as working code) to look into the shape of the schema, or the data, and detect anomalies.