Dualizability in higher Morita categories


Karlsson, E. (2022). Dualizability in higher Morita categories. Perimeter Institute. https://pirsa.org/22100102


Karlsson, Eilind. Dualizability in higher Morita categories. Perimeter Institute, Oct. 07, 2022, https://pirsa.org/22100102


          @misc{ pirsa_22100102,
            doi = {10.48660/22100102},
            url = {https://pirsa.org/22100102},
            author = {Karlsson, Eilind},
            keywords = {Mathematical physics},
            language = {en},
            title = {Dualizability in higher Morita categories},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {oct},
            note = {PIRSA:22100102 see, \url{https://pirsa.org}}

Eilind Karlsson Technical University of Munich (TUM)


The Morita 2-category has as objects associative algebras, 1-morphisms are bimodules and 2-morphisms are given by bimodule homomorphisms. Equivalent objects in this category are exactly Morita equivalent algebras. A vast generalisation of this as a higher category is the so-called higher Morita category, denoted Alg_n. It has two constructions, one due to Haugseng, and one due to Scheimbauer which uses (constructible) factorization algebras. In the latter, Gwilliam-Scheimbauer has proven that every object of Alg_n is n-dualizable. Hence, by the Cobordism Hypothesis, every object gives rise to an n-dimensional (fully extended framed) topological field theory. A natural question to ask is “Which objects of Alg_n are also (n+1)-dualizable?”. This talk is on work in progress (for n=2) to prove a conjecture due to Lurie answering this question. 

Zoom link: https://pitp.zoom.us/j/98595913913?pwd=Vlo1aWtXVlZBVjYxNFlTM2VZY2s3Zz09