Related papers: Monoidal envelopes and Grothendieck construction f…

We describe a fully faithful embedding of the category of (reflexive) globular sets into the category of counital cosymmetric $R$-coalgebras when $R$ is an integral domain. This embedding is a lift of the usual functor of $R$-chains and the…

We describe the multiplicative structures that arise on categories of equivariant modules over certain equivariant commutative ring spectra. Building on our previous work on N-infinity ring spectra, we construct categories of equivariant…

We establish monoidal model structures on model categories of filtered chain complexes constructed by Cirici, Egas Santander, Livernet and Whitehouse whose weak equivalences are the quasi-isomorphisms on the $r$-page of the associated…

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 both from splicing extensions (leading to…

Let $A$ be an algebra in a monoidal category $\Cc$, and let $X$ be an object in $\Cc$. We study $A$-(co)ring structures on the left $A$-module $A\ot X$. These correspond to (co)algebra structures in $EM(\Cc)(A)$, the Eilenberg-Moore…

This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.

An extension of order theory is presented that serves as a formalism for the study of dendroidal sets analogously to way the formalism of order theory is used in the study of simplicial sets.

We observe that the existence of sequential and parallel composition supermaps in higher order theories of transformations can be formalised using enriched category theory. Encouraged by relevant examples such as unitary supermaps and…

Many homotopy-coherent algebraic structures can be described by Segal-type limit conditions determined by an "algebraic pattern", bywhich we mean an $\infty$-category equipped with a factorization system and a collection of "elementary"…

We define a notion of homotopy Segal cooperad in the category of $ E_\infty $-algebras. This model of Segal cooperad that we define in the paper, which we call homotopy Segal $ E_\infty $-Hopf cooperad, covers examples given by the cochain…

For a discrete colored operad $P$, we construct an adjunction between the category of dendroidal sets over the nerve of $P$ and the category of simplicial $P$-algebras, and prove that when $P$ is $\Sigma$-free it establishes a Quillen…

The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a…

In this paper, we address the construction of homotopy bicategories of $(\infty,2)$-categories, which we take as being modeled by 2-fold Segal spaces. Our main result is the concrete construction of a functor $h_2$ from the category of…

We develop the theory of module categories over a Grothendieck-Verdier category, i.e. a monoidal category with a dualizing object and hence a duality structure more general than rigidity. Such a category C comes with two monoidal structures…

Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can…

We introduce a monoidal analogue of Jantzen filtrations in the framework of monoidal abelian categories with generic braidings. It leads to a deformation of the multiplication of the Grothendieck ring. We conjecture, and we prove in many…

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…

In this paper, we compare several functors which take simplicial categories or model categories to complete Segal spaces, which are particularly nice simplicial spaces which, like simplicial categories, can be considered to be models for…

In this chapter we survey some particular topics in category theory in a somewhat unconventional manner. Our main focus will be on monoidal categories, mostly symmetric ones, for which we propose a physical interpretation. These are…

We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category $\mathrm{\underline{Re}p}(S_t)$, to the Heisenberg category. We show that the induced map on Grothendieck rings is injective and…