منابع مشابه
On lifting of biadjoints and lax algebras
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, ...
متن کاملTopological Features of Lax Algebras
Having as starting point Barr’s description of topological spaces as lax algebras for the ultrafilter monad [2], in this paper we present further topological examples of lax algebras – such as quasi-metric spaces, approach spaces and quasi-uniform spaces – and show that, in a suitable setting, the categories of lax algebras have indeed a topological nature. Furthermore, we generalize to this se...
متن کاملCanonical and Op-canonical Lax Algebras
The definition of a category of (T,V)-algebras, where V is a unital commutative quantale and T is a Set-monad, requires the existence of a certain lax extension of T. In this article, we present a general construction of such an extension. This leads to the formation of two categories of (T,V)-algebras: the category Alg(T,V) of canonical (T,V)-algebras, and the category Alg(T′,V) of op-canonica...
متن کاملExtensions in the theory of lax algebras
Recent investigations of lax algebras—in generalization of Barr’s relational algebras—make an essential use of lax extensions of monad functors on Set to the category Rel(V) of sets and V-relations (where V is a unital quantale). For a given monad there may be many such lax extensions, and different constructions appear in the literature. The aim of this article is to shed a unifying light on t...
متن کاملA Kleisli-based Approach to Lax Algebras
By exploiting the description of topological spaces by either neighborhood systems or filter convergence, we obtain a neighborhood-like presentation of categories of lax algebras. The simplicity of this presentation pinpoints the importance of the Kleisli extension, which is introduced as a particular lax extension of the associated monad functor.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2002
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(02)00141-x