Polynomial functors and polynomial monads
Category Theory
2015-05-13 v2
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.
Cite
@article{arxiv.0906.4931,
title = {Polynomial functors and polynomial monads},
author = {Nicola Gambino and Joachim Kock},
journal= {arXiv preprint arXiv:0906.4931},
year = {2015}
}
Comments
41 pages, latex, 2 ps figures generated at runtime by the texdraw package (does not compile with pdflatex). v2: removed assumptions on sums, added short discussion of generalisation, and more details on tensorial strength.