universal construction

The universal constructions in category theory include

Each of these may be defined by requiring it to satisfy a universal property. A universal property is a property of some construction which boils down to (is manifestly equivalent to) the property that an associated object is a universal initial object of some (auxiliary) category.

In good cases, every single one of these is a special case of every other, so somehow one single concept here comes to us with many different faces.

Some or all of these have analogs in higher category theory, notably in 2-category theory and (∞,1)-category theory:

Revised on October 29, 2013 09:37:10 by David Corfield (