  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. The geometry
of a schema is a way of keeping track of relationships between distinct tables,
and can be thought of as a system of foreign keys. The shape of a schema is
generally intuitive (e.g. the schema for round-trip flights is a circle
consisting of an edge from $A$ to $B$ and an edge from $B$ to $A$), and as
such, may be useful for analyzing data.
  We give several applications of our approach, as well as possible advantages
it has over the relational model. We also indicate some directions for further
research.
