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. Copyright © 2012 Cambridge Philosophical Society.
|Mathematical Proceedings of the Cambridge Philosophical Society
|Published - 1 Jan 2013