Related papers: Eilenberg-Moore Bicategories for Opmonoidal Pseudo…

We put a model structure on a full subcategory of based multicategories in which the weak equivalences are created by the K-theory functor of Elmendorf-Mandell, providing a model categorical lift of Thomason's theorem on the modeling of…

Liftable pairs of adjoint functors between braided monoidal categories in the sense of \cite{GV-OnTheDuality} provide auto-adjunctions between the associated categories of bialgebras. Motivated by finding interesting examples of such pairs,…

We introduce and study Hopf monads on autonomous categories (i.e., monoidal categories with duals). Hopf monads generalize Hopf algebras to a non-braided (and non-linear) setting. Indeed, any monoidal adjunction between autonomous…

Skew monoidal categories are monoidal categories with non-invertible `coherence' morphisms. As shown in a previous paper bialgebroids over a ring R can be characterized as the closed skew monoidal structures on the category Mod R in which…

Let $B$ be a bialgebra, and $A$ a left $B$-comodule algebra in a braided monoidal category $\Cc$, and assume that $A$ is also a coalgebra, with a not-necessarily associative or unital left $B$-action. Then we can define a right $A$-action…

We collect some isomorphisms of categories and bijections of structures using the Kleisli and Eilenberg-Moore 2-adjunctions.

We start from any small strict monoidal braided Ab-category and extend it to a monoidal nonstrict braided Ab-category which contains braided bialgebras. The objects of the original category turn out to be modules for these bialgebras

We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…

In this paper we present cartesian structure for symmetric Gray-monoidal double categories. To do this we first introduce locally cubical Gray categories, which are three-dimensional categorical structures analogous to classical, locally…

We compare several recent approaches to studying right Bousfield localization and algebras over monads. We prove these approaches are equivalent, and we apply this equivalence to obtain several new results regarding right Bousfield…

We introduce a tensor product for symmetric monoidal categories with the following properties. Let SMC denote the 2-category with objects small symmetric monoidal categories, arrows symmetric monoidal functors and 2-cells monoidal natural…

This paper proves three different coherence theorems for symmetric monoidal bicategories. First, we show that in a free symmetric monoidal bicategory every diagram of 2-cells commutes. Second, we show that this implies that the free…

We consider commutative Frobenius pseudomonoids in the bicategory of spans, and we show that they are in correspondence with 2-Segal cosymmetric sets. Such a structure can be interpreted as a coherent 2-dimensional topological quantum field…

We assemble polynomials in a locally cartesian closed category into a tricategory, allowing us to define the notion of a polynomial pseudomonad and polynomial pseudoalgebra. Working in the context of natural models of type theory, we prove…

In previous work by the first two authors, Frobenius and commutative algebra objects in the category of spans of sets were characterized in terms of simplicial sets satisfying certain properties. In this paper, we find a similar…

We first introduce the notion of Doi Hom-Hopf modules and find the sufficient condition for the category of Doi Hom-Hopf modules to be monoidal. Also we obtain the condition for the monoidal Hom-algebra and monoidal Hom-coalgebra to be…

We survey the theory of Hopf monads on monoidal categories, and present new examples and applications. As applications, we utilise this machinery to present a new theory of cross products, as well as analogues of the Fundamental Theorem of…

We define the monoidal category $(Poly_E,y,\triangleleft)$ of polynomials under composition in any category $E$ with finite limits, including both cartesian and vertical morphisms of polynomials, and generalize to this setting the Dirichlet…

We treat the problem of lifting bicategories into double categories through categories of vertical morphisms. We make use of a specific instance of the Grothendieck construction to provide, for every bicategory equipped with a possible…

A general notion of operad is given, which includes as instances, the operads originally conceived to study loop spaces, as well as the higher operads that arise in the globular approach to higher dimensional algebra. In the framework of…