Given a pseudomonad $mathcal{T} $ on a $2$-category $mathfrak{B} $, if a right biadjoint $mathfrak{A}tomathfrak{B} $ has a lifting to the pseudoalgebras $mathfrak{A}tomathsf{Ps}textrm{-}mathcal{T}textrm{-}mathsf{Alg} $ then this lifting is also right biadjoint provided that $mathfrak{A} $ has codescent objects. In this paper, we give  general results on lifting of biadjoints. As a consequence, ...

Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in cite{zhang-laan}, we characterize their subalgebras and quotients, and following...

these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

Let V be a vertex operator algebra and g an automorphism of order T . We construct a sequence of associative algebras Ag,n(V ) with n ∈ 1 T Z nonnegative such that Ag,n(V ) is a quotient of Ag,n+1/T (V ) and a pair of functors between the category of Ag,n(V )-modules which are not Ag,n−1/T (V )-modules and the category of admissible V -modules. These functors exhibit a bijection between the sim...

An Eilenberg–like theorem is shown for algebras on a given monad. The main idea is to explore the approach given by Bojańczyk that defines, for a given monad T on a category D, pseudovarieties of T–algebras as classes of finite T–algebras closed under homomorphic images, subalgebras, and finite products. To define pseudovarieties of recognizable languages, which is the other main concept for an...

in this paper, the main results are:a study of the finitely generated mv-algebras of continuous functions from the n-th power of the unit real interval i to i;a study of hopfian mv-algebras; anda category-theoretic study of the map sending an mv-algebra as above to the range of its generators (up to a suitable form of homeomorphism).

a ≤ b iff a is the supremum of the subset {a} ∩ {b}. On any elementary topos E , one has the functor which to an object A associates the object TA = Ã which classifies partial maps into A (cf e.g. [J] 1.2). This functor T carries a monad structure T= (T, η, μ) ; it is a submonad of the power ”set” monad P= (P, η, μ), as described in, say, [AL],[Mi], or [J] 5.3. We shall analyze the category of ...

Categories of lax (T, V )-algebras are shown to have pullbackstable coproducts if T preserves inverse images. The general result not only gives a common proof of this property in many topological categories but also shows that important topological categories, like the category of uniform spaces, are not presentable as a category of lax (T, V )-algebras, with T preserving inverse images. Moreov...