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.Comment: 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