Related papers: Duality for coalgebras for Vietoris and monadicity
As a development of [2] and [3], we construct a "VN-bialgebra" in Vect_k for each k-linear split-semigroupal functor from a suitable monoidal category C to Vect_k. The main aim here is to avoid the customary compactness assumptions on…
Even a functor without an adjoint induces a monad, namely, its codensity monad; this is subject only to the existence of certain limits. We clarify the sense in which codensity monads act as substitutes for monads induced by adjunctions. We…
We investigate cases where the finite dual coalgebra of a twisted tensor product of two algebras is a cotwisted tensor product of their respective finite dual coalgebras. This is achieved by interpreting the finite dual as a topological…
We study some topological spaces that can be considered as hyperspaces associated to noncommutative spaces. More precisely, for a NC compact space associated to a unital C*-algebra, we consider the set of closed projections of the second…
It is known by results of Dyckerhoff-Kapranov and of G\'alvez--Carrillo-Kock-Tonks that the output of the Waldhausen S.-construction has a unital 2-Segal structure. Here, we prove that a certain S.-functor defines an equivalence between the…
It is a classical result of categorical algebra, due to Lawvere and Linton, that finitary varieties of algebras (in the sense of Birkhoff) are dually equivalent to finitary monads on $Set$. Recent work of Ad\'amek, Dost\'al, and Velebil has…
We present a finitary version of Moss' coalgebraic logic for $T$-coalgebras, where $T$ is a locally monotone endofunctor of the category of posets and monotone maps. The logic uses a single cover modality whose arity is given by the least…
It has been known since the work of Duskin and Pelletier four decades ago that KH^op, the category opposite to compact Hausdorff spaces and continuous maps, is monadic over the category of sets. It follows that KH^op is equivalent to a…
The topic of this paper is a generalization of Tannaka duality to coclosed categories. As an application we prove reconstruction theorems for coalgebras (and bialgebras) in categories of topological vector spaces over a nonarchimedean field…
It is shown that the multiplicative monoids of Temperley-Lieb algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a self-adjunction is found in a…
We show that the (co)endomorphism algebra of a sufficiently separable "fibre" functor into Vect_k, for k a field of characteristic 0, has the structure of what we call a "unital" von Neumann core in Vect_k. For Vect_k, this particular…
We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…
We develop the Tannaka-Krein duality for monoidal functors with target in the categories of bimodules over a ring. The $\coend$ of such a functor turns out to be a Hopf algebroid over this ring. Using the result of a previous paper we…
In our previous article [arXiv:1607.06041], we established an equivalence between pointed pivotal module tensor categories and anchored planar algebras. This article introduces the notion of unitarity for both module tensor categories and…
For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalization of Enochs' result for a commutative noetherian ring. As a…
This is the second half of a two-part series studying tensor categories of unitary vertex operator algebras from a unitary point of view.
We present a simple and intuitive framework for duality of locally compacts groups, which is not based on the Haar measure. This is a map, functorial on a non-degenerate subcategory, on the category of coinvolutive Hopf \cst-algebras, and a…
This is the first part in a two-part series of papers constructing a unitary structure for the modular tensor category (MTC) associated to a unitary rational vertex operator algebra (VOA).
We generalize a result of Freedman and He, concerning the duality of moduli and capacities in solid tori, to sufficiently regular metric spaces. This is a continuation of the work of the author and K. Rajala on the corresponding duality in…
Taking inspiration from the monadicity of complete atomic Boolean algebras, we prove that profinite modal algebras are monadic over Set. While analyzing the monadic functor, we recover the universal model construction - a construction…