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.

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