2025/02/25 by Raphael Bennett‐Tennenhaus, Isambard Goodbody, Bennett-Tennenhaus, Raphael +5 · 1 citation
Mathematics · #18A23 #18G80 #18G99 (Secondary) #18M05 (Primary) 18E05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2502.18257
openalex publication_date 2025/02/25 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28
A tensor extriangulated category is an extriangulated category with a symmetric monoidal structure that is compatible with the extriangulated structure. To this end we define a notion of a biextriangulated functor A × B → C, with compatibility conditions between the components. We have two versions of compatibility conditions, the stronger depending on the higher extensions of the extriangulated categories. We give many examples of tensor extriangulated categories. Finally, we generalise Balmer's classification of thick tensor ideals to tensor extriangulated categories.