Related papers: Weak vertical composition
For a weakly mixing bounded rank-one construction the disjointness of its powers is proved. For non-rigid constructions we get minimal self-joinings. Examples of non-mixing rank one actions with explicit weak closure are proposed.
The notion of a weak duality involution on a bicategory was recently introduced by Shulman in [arXiv:1606.05058]. We construct a weak duality involution on the fully dualisable part of $\text{Alg}$, the Morita bicategory of…
Tannaka Duality describes the relationship between algebraic objects in a given category and their representations; an important case is that of Hopf algebras and their categories of representations; these have strong monoidal forgetful…
We construct a strict pivotal monoidal category $\mathcal{D}_{\mathrm{DNA}}$ whose objects are DNA sequences (words over $\{A,C,G,T\}$) and whose morphisms are isotopy classes of typed noncrossing planar matchings, composed of…
We introduce semidirect products of skew monoidal categories as a categorification of semidirect products of monoids (or, perhaps more familiarly, of groups). We also discuss how this construction interacts with monoidal, autonomous and…
We introduce the condensed fiber product of two $G$-crossed braided fusion categories, generalizing existing constructions in the literature. We show that this product is closely related to the cohomological construction known as zesting.…
We provide conditions on a monoidal model category $\mathcal{M}$ so that the category of commutative monoids in $\mathcal{M}$ inherits a model structure from $\mathcal{M}$ in which a map is a weak equivalence or fibration if and only if it…
This note informally describes a way to build certain cubical n-categories by iterating a process of taking models of certain finite limits theories. We base this discussion on a construction of "double bicategories" as bicategories…
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…
The homotopy category of a model structure on a weakly idempotent complete additive category is proved to be equivalent to the additive quotient of the category of cofibrant-fibrant objects with respect to the subcategory of…
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…
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…
We give a framework for comparing on the one hand theories of n-categories that are weakly enriched operadically, and on the other hand n-categories given as algebras for a contractible globular operad. Examples of the former are the…
An algebra $A$ is left weakly Gorenstein if any semi-Gorenstein-projective left $A$-modules is Gorenstein-projective. The weakly Gorensteinness of two kinds of algebras are answered. Using the method of the monomorphism category, it is…
Classical definitions of weak higher-dimensional categories are given inductively; for example, a bicategory has a set of objects and hom categories, and a tricategory has a set of objects and hom bicategories. However, more recent…
We lay the foundations for a theory of quasi-categories in a monoidal category $\mathcal{V}$ replacing $\mathrm{Set}$, aimed at realising weak enrichment in the category $S\mathcal{V}$ of simplicial objects in $\mathcal{V}$. To accomodate…
We investigate the extent to which the weak equivalences in a model category can be equipped with algebraic structure. We prove, for instance, that there exists a monad T such that a morphism of topological spaces admits T-algebra structure…
We define a tricategory T of length 3 complexes of abelian sheaves, whose hom-bigroupoids consist of weak morphisms of such complexes. We also define a 3-category 2PIC(S) of Picard 2-stacks, whose hom-2-groupoids consist of additive…
We study monoidal 2-categories and bicategories in terms of categorical extensions and the cohomological data they determine in appropriate cohomology theories with coefficients in Picard groupoids. In particular, we analyze the hierarchy…
The centre of a monoidal category is a braided monoidal category. Monoidal categories are monoidal objects (or pseudomonoids) in the monoidal bicategory of categories. This paper provides a universal construction in a braided monoidal…