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- W2952955512 abstract "We define a cohomology for an arbitrary $K$-linear semistrict semigroupal 2-category $(mathfrak{C},otimes)$ (called in the paper a Gray semigroup) and show that its first order (unitary) deformations, up to the suitable notion of equivalence, are in one-one correspondence with the elements of the second cohomology group. Fundamental to the construction is a double complex, similar to Gerstenhaber-Schack's double complex for bialgebras. We also identify the cohomologies describing separately the deformations of the tensor product, the associator and the pentagonator. To obtain these results, a cohomology theory for an arbitrary $K$-linear unitary pseudofunctor is introduced describing its purely pseudofunctorial deformations, and generalizing Yetter's cohomology for semigroupal functors. The corresponding higher order obstructions will be considered in a future paper." @default.
- W2952955512 created "2019-06-27" @default.
- W2952955512 creator A5059336327 @default.
- W2952955512 date "2002-04-09" @default.
- W2952955512 modified "2023-09-27" @default.
- W2952955512 title "Cohomology and deformation theory of monoidal 2-categories I" @default.
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