Related papers: Skew monoidal structures on actegories
If $\mathcal{C}$ is a cocomplete monoidal category in which tensoring from both sides preserves coequalizers, then the category of monoids over $\mathcal{C}$ is cocomplete. The same holds if $\mathcal{C}$ has regular factorizations and…
We identify natural symmetries of each rigid higher braided category. Specifically, we construct a functorial action by the continuous group $\Omega \mathsf{O}(n)$ on each $\mathcal{E}_{n-1}$-monoidal $(g,d)$-category $\mathcal{R}$ in which…
We introduce the notion of solid monoid and rigid monoid in monoidal categories and study the formal properties of these objects in this framework. We show that there is a one to one correspondence between solid monoids, smashing…
We demonstrate that categories of continuous actions of topological monoids on discrete spaces are Grothendieck toposes. We exhibit properties of these toposes, giving a solution to the corresponding Morita-equivalence problem. We…
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal monads and comonads, i.e. monads and comonads in a monoidal category such that the endofunctor of the monad or comonad is a monoidal functor…
We show that braided, sylleptic and symmetric monoidal bicategories are precisely the $\mathsf{E}_k$-monoids in the cartesian monoidal $(\infty,1)$-category of bicategories for respective integers $k$. To manage the underlying computations,…
We give a method to construct new self-adjoint representations of the braid group. In particular, we give a family of irreducible self-adjoint representations of dimension arbitrarily large. Moreover we give sufficient conditions for a…
A near-group category is an additively semisimple category with a product such that all but one of the simple objects is invertible. We classify braided structures on near-group categories, and give explicit numerical formulas for their…
In this document, we collect a list of categorical structures on the category $\mathbf{Poly}$ of polynomial functors. There is no implied claim that this list is in any way complete. It includes: infinitely many monoidal structures, all but…
We give a new criterion guaranteeing existence of model structures left-induced along a functor admitting both adjoints. This works under the hypothesis that the functor induces idempotent adjunctions at the homotopy category level. As an…
We prove that the action of a generalized braid group on an enhanced triangulated categories, generated by spherical twist functors along an ADE-configuration of $\omega$-spherical objects, is faithful for any integer $\omega \neq 1$.
A monoidal model category is a model category with a compatible closed monoidal structure. Such things abound in nature; simplicial sets and chain complexes of abelian groups are examples. Given a monoidal model category, one can consider…
We detail a construction of a symmetric monoidal structure, called the reduced tensor product on the 2-category of braided tensor categories $\mathbf{BTC}(\mathcal{A})$ containing a fixed symmetric fusion subcategory $\mathcal{A}$. The…
It is common to encounter symmetric monoidal categories $\mathcal{C}$ for which every object is equipped with an algebraic structure, in a way that is compatible with the monoidal product and unit in $\mathcal{C}$. We define this formally…
It is well-known that the category of Kleisli algebras for a monoidal monad carries a canonical monoidal structure. We define the notion of a commutative graded monad and present a strictly two-categorical proof that Kleisli algebras for…
It is shown that the multiplicative monoids of Brauer's centralizer algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself, and where, moreover, a kind of…
We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized $K$-theoretic Coulomb branch. As a consequence, we see that our skein algebra arises…
Let $\mathcal C$ be a category with finite colimits, writing its coproduct $+$, and let $(\mathcal D, \otimes)$ be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided monoidal…
Given an action of a finite group on a triangulated category with a suitable strong exceptional collection, a construction of Elagin produces an associated strong exceptional collection on the equivariant category. We prove that the…
We study toposes of actions of monoids on sets. We begin with ordinary actions, producing a class of presheaf toposes which we characterize. As groundwork for considering topological monoids, we branch out into a study of supercompactly…