8 research outputs found
The Combinatorics of Polynomial Functors
We propose a new description of Endofunctors of Module Categories, based upon
a combinatorial category comprising finite sets and so-called mazes. Polynomial
and numerical functors both find a natural interpretation in this frame-work.
Since strict polynomial functors, according to the work of Salomonsson, are
encoded by multi-sets, the two strains of functors may be compared and
contrasted through juxtaposing the respective combinatorial structures, leading
to the Polynomial Functor Theorem, giving an effective criterion for when a
numerical (polynomial) functor is strict polynomial
Polynomial Functors of Modules
We introduce the notion of numerical functors to generalise Eilenberg &
MacLane's polynomial functors to modules over a binomial base ring. After
shewing how these functors are encoded by modules over a certain ring, we
record a precise criterion for a numerical (or polynomial) functor to admit a
strict polynomial structure in the sense of Friedlander & Suslin. We also
provide several characterisations of analytic functors