Olynomials in categories with pullbacks

Abstract

The theory developed by Gambino and Kock, of polynomials over a locally cartesian closed category ε, is generalised for ε just having pullbacks. The 2-categorical analogue of the theory of polynomials and polynomial functors is given, and its relationship with Street’s theory of fibrations within 2-categories is explored. Johnstone’s notion of “bagdomain data” is adapted to the present framework to make it easier to completely exhibit examples of polynomial monads.