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- M Ern, J Koslowski, A Melton, G E Strecker
- 1992

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)

- JÜRGEN KOSLOWSKI
- 1997

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)

- J. Robin B. Cockett, Jürgen Koslowski, R. A. G. Seely
- Mathematical Structures in Computer Science
- 2000

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)

- Gabriele Castellini, Jürgen Koslowski, George E. Strecker
- Applied Categorical Structures
- 1994

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)

- J R B Cockett, J Koslowski, R A G Seely
- 1995

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)

0. INTRODUCTION Closure operators are well-known in topology and order theory. In the setting of an hE; Mi-category for sinks we show that the categorical abstraction of the notion of closure operator is such that closure operators appear as essentially the xed points (i.e., as the Galois-closed members) of a natural Galois connection. We identify a common… (More)

- Jürgen Koslowski
- Electr. Notes Theor. Comput. Sci.
- 2002

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)

The Galois connection given in 1985 by Pumpl un and RR ohrl between the classes of objects and the classes of morphisms in any category is shown (under ordinary circumstances) to have a \natural" factorization through the system of all idempotent closure operators over the category. Furthermore, each \component" of the factorization is a Galois connection… (More)

- Jürgen Koslowski
- Theor. Comput. Sci.
- 1997

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)

- Jürgen Koslowski
- Applied Categorical Structures
- 2001