The Γ-structure of an additive track category

2009/12/23 by Gérald Gaudens, Gaudens, Gérald
Mathematics · #18G55 #55U99 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:18G55 #msc:55U99

paper · pdf · doi:10.48550/arxiv.0912.4673

arxiv created 2009/12/23 · arxiv updated 2010/01/14

Abstract

We prove that an additive track category with strong coproducts is equivalent to the category of pseudomodels for the algebraic theory of \nil₂ 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.

Related

• Abelian categories and definable additive categories
• Categories of imaginaries for definable additive categories
• Enriched model categories and an application to additive endomorphism spectra
• Categories as models on a suitable algebraic theory
• Strengthening track theories