## 16 Citations

### Graded Leinster monoids and generalized Deligne conjecture for 1-monoidal abelian categories

- Mathematics
- 2015

In our recent paper [Sh1] a version of the "generalized Deligne conjecture" for abelian $n$-fold monoidal categories is proven. For $n=1$ this result says that, given an abelian monoidal $k$-linear…

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

- Mathematics
- 2018

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…

### The $B_\infty$-structure on the derived endomorphism algebra of the unit in a monoidal category

- Mathematics
- 2019

Consider a monoidal category which is at the same time abelian with enough projectives and such that projectives are flat on the right. We show that there is a $B_{\infty}$-algebra which is…

### The B∞-Structure on the Derived Endomorphism Algebra of the Unit in a Monoidal Category

- MathematicsInternational Mathematics Research Notices
- 2021

Consider a monoidal category that is at the same time abelian with enough projectives and such that projectives are flat on the right. We show that there is a $B_{\infty }$-algebra that is…

### On the twisted tensor product of small dg categories

- MathematicsJournal of Noncommutative Geometry
- 2020

Given two small dg categories $C,D$, defined over a field, we introduce their (non-symmetric) twisted tensor product $C\overset{\sim}{\otimes} D$. We show that $-\overset{\sim}{\otimes} D$ is left…

### Linear quasi-categories as templicial modules.

- Mathematics
- 2020

We introduce a notion of enriched $\infty$-categories over a suitable monoidal category, in analogy with quasi-categories over the category of sets. We make use of certain colax monoidal functors,…

### Graded Lie structure on cohomology of some exact monoidal categories

- Mathematics
- 2020

For some exact monoidal categories, we describe explicitly a connection between topological and algebraic definitions of the Lie bracket on the extension algebra of the unit object. The topological…

### Brackets and products from centres in extension categories

- Mathematics
- 2021

Building on Retakh’s approach to Ext groups through categories of extensions, Schwede reobtained the well-known Gerstenhaber algebra structure on Ext groups over bimodules of associative algebras…

### Cyclic Gerstenhaber–Schack cohomology

- MathematicsJournal of Noncommutative Geometry
- 2022

We show that the diagonal complex computing the Gerstenhaber-Schack cohomology of a bialgebra (that is, the cohomology theory governing bialgebra deformations) can be given the structure of an operad…

### On Evrard's homotopy fibrant replacement of a functor

- Mathematics
- 2016

We provide a more economical refined version of Evrard’s categorical cocylinder factorization of a functor [Ev1,2]. We show that any functor between small categories can be factored into a homotopy…

## References

SHOWING 1-10 OF 51 REFERENCES

### A proof of the generalized Deligne conjecture for 1-monoidal abelian categories

- Mathematics
- 2015

In our recent paper [Sh1] a version of the "generalized Deligne conjecture" for abelian $n$-fold monoidal categories is proven, with some uncommon algebraic objects called Leinster $(n+1)$-algebras…

### Hopf algebras, tetramodules, and n-fold monoidal categories

- Mathematics
- 2009

The abelian category of tetramodules over an associative bialgebra $A$ is related with the Gerstenhaber-Schack (GS) cohomology as $Ext_\Tetra(A,A)=H_\GS(A)$. We construct a 2-fold monoidal structure…

### Monoidal cofibrant resolutions of dg algebras

- Mathematics
- 2011

Let $k$ be a field of any characteristic. In this paper, we construct a functorial cofibrant resolution $\mathfrak{R}(A)$ for the $\mathbb{Z}_{\le 0}$-graded dg algebras $A$ over $k$, such that the…

### Higher Hochschild cohomology, Brane topology and centralizers of $E_n$-algebra maps

- Mathematics
- 2012

We use factorization homology and higher Hochschild (co)chains to study various problems in algebraic topology and homotopical algebra, notably brane topology, centralizers of $E_n$-algebras maps and…

### Homotopy types of strict 3-groupoids

- Mathematics
- 1998

We look at strict $n$-groupoids and show that if $\Re$ is any realization functor from the category of strict $n$-groupoids to the category of spaces satisfying a minimal property of compatibility…

### The tangent complex and Hochschild cohomology of $\mathcal {E}_n$-rings

- MathematicsCompositio Mathematica
- 2012

Abstract In this work, we study the deformation theory of ${\mathcal {E}}_n$-rings and the ${\mathcal {E}}_n$ analogue of the tangent complex, or topological André–Quillen cohomology. We prove a…

### Tetramodules Over a Bialgebra Form a 2-fold Monoidal Category

- MathematicsAppl. Categorical Struct.
- 2013

It is proved that the category of tetramodules over any bialgebra B is a 2-fold-monoidal category, with B a unit object in it, and it is implied that RHom ∙ (B,B) in thecategory of tetamodules is naturally a homotopy 3-algebra.

### Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture

- MathematicsCompositio Mathematica
- 2004

We show that if $(M,\otimes,I)$ is a monoidal model category then $\mathbb{R}\underline{\rm End}_{M}(I)$ is a (weak) 2-monoid in sSet. This applies in particular when M is the category of A-bimodules…