# A proof of the contractibility of the 2-operad defined via the twisted tensor product

@article{Shoikhet2019APO, title={A proof of the contractibility of the 2-operad defined via the twisted tensor product}, author={Boris Shoikhet}, journal={arXiv: Quantum Algebra}, year={2019} }

In our recent papers [Sh1,2], we introduced a {\it twisted tensor product} of dg categories, and provided, in terms of it, {\it a contractible 2-operad $\mathcal{O}$}, acting on the category of small dg categories, in which the "natural transformations" are derived. We made use of some homotopy theory developed in [To] to prove the contractibility of the 2-operad $\mathcal{O}$. The contractibility is an important issue, in vein of the theory of Batanin [Ba1,2], according to which an action of a…

## One Citation

### The twisted tensor product of dg categories and a contractible 2-operad

- Mathematics
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It is well-known that the "pre-2-category" $\mathscr{C}at_\mathrm{dg}^\mathrm{coh}(k)$ of small dg categories over a field $k$, with 1-morphisms defined as dg functors, and with 2-morphisms defined…

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