Related papers: Simplicial effects and weakly associative partial …

We introduce and study a general notion of polynomial functor from a small monoidal symmetric category whose unit is an initial object and give a classification result of polynomial functors of degree smaller of equal to n modulo those of…

In this paper we develope a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to…

We show that, under some mild conditions, a bialgebra in an abelian and coabelian braided monoidal category has a weak projection onto a formally smooth (as a coalgebra) sub-bialgebra with antipode; see Theorem 1.12. In the second part of…

A number of properties of spherical Artin groups extend to Garside groups, defined as the groups of fractions of monoids where least common multiples exist, there is no nontrivial unit, and some additional finiteness conditions are…

The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…

In this paper, we build on a recent bicategorical model called thin spans of groupoids, introduced by Clairambault and Forest. Notably, thin spans feature a decomposition of symmetry into two sub-groupoids of polarized -- positive and…

For a Kan complex with a vertex, we have the notion of its simplicial homotopy groups. In this paper, for a weak complicial set in the sense of Verity with a vertex, we construct monoids which are a generalization of simplicial homotopy…

We develop a version of controlled algebra for simplicial rings. This generalizes the methods which lead to successful proofs of the algebraic K- theory isomorphism conjecture (Farrell-Jones Conjecture) for a large class of groups. This is…

The bosonic sector of various supergravity theories reduces to a homogeneous space G/H in three dimensions. The corresponding algebras g are simple for (half-)maximal supergravity, but can be semi-simple for other theories. We extend the…

Although multiplier bimonoids in general are not known to correspond to comonoids in any monoidal category, we classify them in terms of maps from the Catalan simplicial set to another suitable simplicial set; thus they can be regarded as…

To characterize categorical constraints - associativity, commutativity and monoidality - in the context of quasimonoidal categories, from a cohomological point of view, we define the notion of a parity (quasi)complex. Applied to groups…

We produce a highly structured way of associating a simplicial category to a model category which improves on work of Dwyer and Kan and answers a question of Hovey. We show that model categories satisfying a certain axiom are Quillen…

We consider the category of C*-algebras equipped with actions of a locally compact quantum group. We show that this category admits a monoidal structure satisfying certain natural conditions if and only if the group is quasitriangular. The…

This paper continues the development of a simplicial theory of weak omega-categories, by studying categories which are enriched in weak complicial sets. These complicial Gray-categories generalise both the Kan complex enriched categories of…

We prove that arbitrary simplicial manifolds satisfy Kan conditions in a suitable local sense. This allows us to expand a technique for differentiating higher Lie groupoids worked out in current research to the setting of general simplicial…

We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be…

Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely…

We introduce a notion of quasi-weak equivalences associated with weak-equivalences in an exact category. It gives us a delooping for (idempotent complete) exact categories and a condition that the negative $K$-group of an exact category…

The reduced universal monoid on the action category associated to a pointed simplicial M-set has appeared in the guise of various simplicial monoid and group constructions. These include the classical constructions of Milnor and James, as…

We study observables on monotone $\sigma$-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. The set of sharp elements of a monotone $\sigma$-complete homogeneous…