In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.

The general methodology of “algebraizing” logics (cf. [2], [4]) is used here for combining different logics. The combination of logics is represented as taking the colimit of the constituent logics in the category of algebraizable logics. The cocompleteness of this category as well as its isomorphism to the corresponding category of certain first-order theories are proved. In this paper we tran...

In the theory of operads we consider generalized symmetric power functors defined by sums of coinvariant modules. One observes classically that the symmetric functor construction provides an isomorphism from the category of symmetric modules to a split subcategory of the category of functors on dgmodules (if dg-modules form our ground category). The purpose of this article is to obtain a simila...

Using the isomorphism from [3] between the category Pries of Priestley spaces and the category PStone of pairwise Stone spaces we construct a Vietoris hyperspace functor on the category PStone related to the Vietoris hyperspace functor on the category Pries [4, 18, 24]. We show that the coalgebras for this functor determine a semantics for the positive fragment of modal logic. The sole novelty ...

We define the i-restriction and i-induction functors on the category O of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of a Fock space.

Functors which are determined, up to natural isomorphism, by their values on objects, are called DVO (Defined by Values on Objects). We focus on the collection of polynomial functors on a category of sets (classes), and we give a characterization theorem of the DVO functors over such collection of functors. Moreover, we show that the (κ-bounded) powerset functor is not DVO.

Let V be a complete discrete valuation ring of mixed characteristic. We classify arithmetic D-modules on Spf(V[[t]]) up to certain kind of ‘analytic isomorphism’. This result is used to construct canonical extensions (in the sense of Katz and Gabber) for objects of this category.

We show that Thompson’s group F is the symmetry group of the ‘generic idempotent’. That is, take the monoidal category freely generated by an object A and an isomorphism A ⊗ A A; then F is the group of automorphisms of A.

The simplicial category ∆ plays many roles all over mathematics. In one of these roles it is a monad freely generated by a single object (see [9], Section 3, [2], Section 4, and references therein). That ∆ is isomorphic to this free monad may be understood as a coherence result connecting the syntax brought by the equational presentation of monads and the semantics given by the order preserving...