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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.14545 |
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Table of Contents:
- Let $(\mathcal{C}, \otimes)$ be a monoidal dg-category. We construct a complex controlling the deformation of the monoidal structure on $\mathcal{C}$ together with the deformation of the underlying dg-category itself. We show that in the case of a semisimple category $\mathcal{C}$ it reduces to the Davydov-Yetter complex. Furthermore, we study this complex in several special cases, in particular, in the case of the category of $A$-modules over a commutative algebra $A$ we obtain a complex computing operadic $E_2$-cohomology of $A$. And in the case of the category of representations of an associative bialgebra we recover the Gerstenhaber-Schack complex. In the latter case our construction can be considered as a generalization of the Gerstenhaber-Schack complex to quasi-bialgebras.