Databases

Categories and functors without admitting it.

Spivak uses databases to build up intuition for the introduction of categories.

Table

Let a table be associated with a structure for recording data corresponding to scientific observations of some kind.

• A table has rows and columns. Its existence suggests a way to observe events and record types of observations.
• The rows are discrete events. Alternatively, rows can represent discrete objects.
• The columns are types of observations (or different objects).
• A cell is a (row, column) tuple which corresponds to a type of observation for a given event (or object).
• A database has one or more tables.

Primary key

The column c for which all cells (*, c) are unique. One can uniquely identify a row based on the value of an observation from this column.

Foreign key

Links one table to another. It is a column in table A which refers to the primary key column of another table.

Data column

Houses elementary data. If one were to force data columns to be foreign keys, they would be foreign keys into what Spivak calls leaf tables whicha are non-branching.

Database schema

A pair (G, congruence), where G is a graph and congruence is a congruence on G.