Polynomials in categories with pullbacks

Mark Weber

The theory developed by Gambino and Kock, of polynomials over a locally cartesian closed category E, is generalised for E 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.

Keywords: polynomial functors, 2-monads

2010 MSC: 18A05; 18D20; 18D50

Theory and Applications of Categories, Vol. 30, 2015, No. 16, pp 533-598.

Published 2015-05-02.


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