Weihrauch problems as containers

Abstract

We note that Weihrauch problems can be regarded as containers over the category of projective represented spaces and that Weihrauch reductions correspond exactly to container morphisms. We also show that Bauer's extended Weihrauch degrees and the posetal reflection of containers over partition assemblies are equivalent. Using this characterization, we show how a number of operators over Weihrauch degrees, such as the composition product, also arise naturally from the abstract theory of polynomial functors.

26 pages, fixed typos in the statement of Lemma 4