Algebras, modules and the plus construction

Hybrid talk. For zoom details contact Christian Kaiser (kaiser@mpim...).

We give a general plus construction for monoidal categories. The idea behind this is
the opetopic principle of Baez and Dolan. Such a construction allows one to naturally
define modules over algebras generalizing the traditional algebraic setting. There
are several versions of this incorporating symmetries and units. Beside the classical
example a basic example is that of algebras over operads - here the role of algebra
is played by the operad and that of the module by the algebra over the operad.
Both notions are encoded as monoidal functors. The theory has set-theoretic, linear
and categorical perspectives which we will highlight. This work generalizes previous
results on  monoidal functors out of so-called Feynman categories,which includes the
example above, and is joint work with Michael Monaco.