2019/02/13 by Jonathan Lorand, Lorand, Jonathan, Alessandro Valentino +1
Mathematics · #16D90 #18D05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1902.04866
openalex publication_date 2019/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of a weak duality involution on a bicategory was recently introduced by Shulman in [arXiv:1606.05058]. We construct a weak duality involution on the fully dualisable part of Alg, the Morita bicategory of finite-dimensional k-algebras. The 2-category KV of Kapranov-Voevodsky k-vector spaces may be equipped with a canonical strict duality involution. We show that the pseudofunctor Rep: Algfd → KV sending an algebra to its category of finite-dimensional modules may be canonically equipped with the structure of a duality pseudofunctor. Thus Rep is a strictification in the sense of Shulman's strictification theorem for bicategories with a weak duality involution. Finally, we present a general setting for duality involutions on the Morita bicategory of algebras in a semisimple symmetric finite tensor category.