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Polynomial functors and polynomial monads

Published online by Cambridge University Press:  06 September 2012

NICOLA GAMBINO  and
JOACHIM KOCK
NICOLA GAMBINO
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, via Archirafi 34, 90123 Palermo, Italy. e-mail: ngambino@math.unipa.it
JOACHIM KOCK
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain. e-mail: kock@mat.uab.cat
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Abstract

We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a polynomial endofunctor is polynomial. The relationship with operads and other related notions is explored.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 1 , January 2013 , pp. 153 - 192
Copyright
Copyright © Cambridge Philosophical Society 2012

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