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Abstract

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.