Simplicial Databases

Understand

In this paper, we define a category DB, called the category of simplicial databases, whose objects are databases and whose morphisms are data-preserving maps.

• Along the way we give a precise formulation of the category of relational databases, and prove that it is a full subcategory of DB.
• We also prove that limits and colimits always exist in DB and that they correspond to queries such as select, join, union, etc.
• One feature of our construction is that the schema of a simplicial database has a natural geometric structure: an underlying simplicial set.