Jürgen Koslowski

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We provide the rudiments of the theory of Galois connections (or residuation theory, as it is sometimes called) together with many examples and applications. Galois connections occur in profusion and are well-known to most mathematicians who deal with order theory; they seem to be less known to topologists. However, because of their ubiquity and simplicity,(More)
Given a bicategory, Y , with stable local coequalizers, we construct a bicategory of monads Y-mnd by using lax functors from the generic 0-cell, 1-cell and 2-cell, respectively, into Y. Any lax functor into Y factors through Y-mnd and the 1-cells turn out to be the familiar bimodules. The locally ordered bicategory rel and its bicategory of monads both fail(More)
Linear bicategories are a generalization of bicategories, in which the one horizontal composition is replaced by two (linked) horizontal compositions. These compositions provide a semantic model for the tensor and par of linear logic: in particular, as composition is fundamentally noncommutative, they provide a suggestive source of models for noncommutative(More)
In an hE; M i-category X for sinks, we identify necessary conditions for Galois connections from the power collection of the class of (composable pairs) of morphisms in M to factor through the \lattice" of all closure operators on M , and to factor through certain sublattices. This leads to the notion of regular closure operator. As one byproduct of these(More)
Linear bicategories are a generalization of ordinary bicategories in which there are two horizontal (1-cell) compositions corresponding to the " tensor " and " par " of linear logic. Benabou's notion of a morphism (lax 2-functor) of bicategories may be generalized to linear bicategories, where they are called linear functors. Unfortunately, as for the(More)
In the quest for an elegant formulation of the notion of " polycategory " we develop a more symmetric counterpart to Burroni's notion of " T-category " , where T is a cartesian monad on a category X with pullbacks. Our approach involves two such monads, S and T , that are linked by a suitable generalization of a distributive law in the sense of Beck. This(More)
We provide a simple direct proof that for a nitary signature and a set of inequalities the free algebra functor on the category of directed complete partial orders (dcpo's) takes continuous, respectively algebraic, dcpo's to free algebras whose underlying dcpo is again continuous, respectively algebraic. 0 Introduction Consider a nitary signature and a set(More)