English

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.

Keywords

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.

R2 v1 2026-06-21T13:18:16.701Z