B. Shoikhet

collaborators

3 papers

math.QA2025

Generalised Joyal disks and $I^_{d}$ -colored $(d + 1)$ -operads

Boris Shoikhet

In this paper, we propose a method for constructing a colored $(d + 1)$ -operad $seq_{d}$ in $Sets$ , in the sense of Batanin [Ba1,2], whose category of colors (=the ca…

math.CT2024

Twisted tensor product of dg categories and Kontsevich's Swiss Cheese conjecture

Michael Batanin, Boris Shoikhet

Let $A$ be a $1$ -algebra. The Kontsevich Swiss Cheese conjecture [K2] states that the homotopy category $Ho (Act (A))$ of actions of $2$ -algebras on $A$ has a final…

math.QA2024

The category $I^_{2}$ , derived modifications, and deformation theory of monoidal categories

Piergiorgio Panero, Boris Shoikhet

A complex $C^{∙} (C, D) (F, G) (I^\cdot, I^¸)$ , generalising the Davydov-Yetter complex of a monoidal category, is constructed. Here $C, D$ are $k$ -linear (dg) monoidal categories, $F,…

Generalised Joyal disks and I^d​-colored (d+1)-operads

Twisted tensor product of dg categories and Kontsevich's Swiss Cheese conjecture

The category I^2​, derived modifications, and deformation theory of monoidal categories

Generalised Joyal disks and $I^_{d}$ -colored $(d + 1)$ -operads

The category $I^_{2}$ , derived modifications, and deformation theory of monoidal categories