The $\Gamma$-structure of an additive track category

TL;DR

This paper establishes an equivalence between additive track categories with strong coproducts and pseudomodels for $ il_2$ groups, extending classical results about abelian groups to a higher categorical context.

Contribution

It generalizes the classical equivalence between abelian groups and models of their algebraic theory to a broader setting involving $ il_2$ groups and track categories.

Findings

Additive track categories with strong coproducts are equivalent to pseudomodels for $ il_2$ groups.

Dual statements for the theory are also established.

The result extends classical algebraic theory to higher categorical structures.

Abstract

We prove that an additive track category with strong coproducts is equivalent to the category of pseudomodels for the algebraic theory of $\nil_2$ groups. This generalizes the classical statement that the category of models for the algebraic theory of abelian groups is equivalent to the category of abelian groups. Dual statements are also considered.