Timeline for Explicit description of the tensor product of symmetric monoidal categories / Picard groupoids
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 27, 2021 at 3:35 | comment | added | Emily | I've been planning to read these (and now also your paper, which is really lovely!) and will update the question after that (in particular to mention the coherence laws I forgot about). | |
| Aug 27, 2021 at 3:34 | comment | added | Emily | @MartinBrandenburg Thanks, Martin! I asked this on Twitter too, and there Amar Hadzihasanovic mentioned their preprint The smash product of monoidal theories and Hackney–Robertson's On the category of props, giving an outline on adapting the tensor product of PROPs of Hackney–Robertson to get the strict tensor product $\otimes^{\mathsf{str}}_{\mathbb{F}}$. | |
| Aug 26, 2021 at 14:45 | comment | added | Martin Brandenburg | I am pretty sure this only works for small symmetric monoidal categories. We need to categorify the construction of tensor products of commutative monoids. Take the free symmetric monoidal category on the product of the underlying categories and freely adjoin the isomorphisms using bicategorical coequalizers and enforce the coherence laws (which you didn't mention) using bicategorical coequifiers. Thus, the universal constructions in arxiv.org/abs/2001.10123 will be useful. | |
| Aug 20, 2021 at 22:34 | history | asked | Emily | CC BY-SA 4.0 |