Monads are used for various applications in computer science, and well-known is e.g. the interpretation of morphisms in the Kleisli category of the term monad as variable substitutions assigning variables to terms. An application building upon this observation is the equivalence between most general unifiers and co-equalizers in this category [13]. In this paper we will use monads with addition...

There are infinitely many variants of the notion of Kan fibration that, together with suitable choices of cofibrations and the usual notion of weak equivalence of simplicial sets, satisfy Quillen’s axioms for a homotopy model category. The combinatorics underlying these fibrations is purely finitary and seems interesting both for its own sake and for its interaction with homotopy types. To show...

We introduce a new quantum group which is a quantization of the enveloping superalgebra of a twisted affine Lie superalgebra of type Q. We study generators and relations for superalgebras in the finite and twisted affine cases, and also universal central extensions. Afterwards, we apply the FRT formalism to a certain solution of the quantum Yang-Baxter equation to define that new quantum group ...

Prior work towards the subject of higher-dimensional categories gives rise to several examples of a category over Cat to which the slice-category construction can be lifted universally. The present paper starts by supplying this last clause with a precise meaning. It goes on to establish for any such category a certain embedding in a presheaf category, to describe the image, and hence to derive...

Neighbourhood structures are the standard semantic tool used to reason about non-normal modal logics. The logic of all neighbourhood models is called classical modal logic. In coalgebraic terms, a neighbourhood frame is a coalgebra for the contravariant powerset functor composed with itself, denoted by 2 2. We use this coalgebraic modelling to derive notions of equivalence between neighbourhood...

For a scheme X, denote by SH(X_et^hyp) the stabilization of hypercompletion its etale infty-topos, and SH_et(X) localization stable motivic homotopy category SH(X) at (desuspensions of) hypercovers. infty-category C, write C_p^comp for p-completion C. We prove that under suitable finiteness hypotheses, assuming p is invertible on canonical functor e_p^comp: SH(X_et^hyp)_p^comp -> SH_et(X)_p^com...

Throughout this paper k denotes an algebraically closed field, and all algebras considered here are assumed to be basic, connected, finite-dimensional k-algebras with identity. For an algebra Λ, we denote by modΛ and by modΛ the category of finitedimensional (right) Λ-modules and its stable category, respectively. Recall that for two algebras Λ and Π, an equivalence modΛ → modΠ is called a stab...

Abstract Let G denote a possibly discrete topological group admitting an open subgroup I which is pro- p . If H denotes the corresponding Hecke algebra over field k of characteristic , then we study adjunction between -modules and -linear smooth -representations in terms various model structures. Gorenstein ring, single out full subcategory equivalent to category all projective via functor -inv...

Neighbourhood structures are the standard semantic tool used to reason about non-normal modal logics. The logic of all neighbourhood models is called classical modal logic. In coalgebraic terms, a neighbourhood frame is a coalgebra for the contravariant powerset functor composed with itself, denoted by 2. We use this coalgebraic modelling to derive notions of equivalence between neighbourhood s...

We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...