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Conference Paper

Feynman categories and representation theory


Kaufmann,  Ralph M.
Max Planck Institute for Mathematics, Max Planck Society;

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Kaufmann, R. M. (2021). Feynman categories and representation theory. In K. Igusa, A. Martsinkovsky, & G. Todorov (Eds.), Representations of algebras, geometry and physics (pp. 11-84). Providence: American Mathematical Society.

Cite as: https://hdl.handle.net/21.11116/0000-0009-7DEA-4
We give a presentation of Feynman categories from a
representation--theoretical viewpoint.
Feynman categories are a special type of monoidal categories and their
representations are monoidal functors. They can be viewed as a far reaching
generalization of groups, algebras and modules. Taking a new algebraic
approach, we provide more examples and more details for several key
constructions. This leads to new applications and results.
The text is intended to be a self--contained basis for a crossover of more
elevated constructions and results in the fields of representation theory and
Feynman categories, whose applications so far include number theory, geometry,
topology and physics.