On the fractions of semi-Mackey and Tambara functors
Hiroyuki Nakaoka

TL;DR
This paper introduces the concept of fractions of semi-Mackey and Tambara functors, extending algebraic fraction constructions to these $G$-bivariant functors for finite groups.
Contribution
It generalizes the notion of fractions of rings to the setting of semi-Mackey and Tambara functors, providing a new algebraic framework for $G$-bivariant functors.
Findings
Defined the fraction of a Tambara functor by a multiplicative semi-Mackey subfunctor.
Extended algebraic fraction concepts to $G$-bivariant functors.
Provided foundational results for algebraic manipulations of these functors.
Abstract
For a finite group , a semi-Mackey (resp. Tambara) functor is regarded as a -bivariant analog of a commutative monoid (resp. ring). As such, some naive algebraic constructions are generalized to this -bivariant setting. In this article, as a -bivariant analog of the fraction of a ring, we consider {\it fraction} of a Tambara (and a semi-Mackey) functor, by a multiplicative semi-Mackey subfunctor.
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Taxonomy
TopicsRings, Modules, and Algebras · Algebraic structures and combinatorial models · Advanced Topics in Algebra
