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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 E, M-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)

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, Jürgen Koslowski
- 2006

A. The cyclic Chu-construction for closed bicategories with pullbacks, which generalizes the original Chu-construction for symmetric monoidal closed categories, turns out to have a non-cyclic counterpart. Both use so-called Chu-spans as new 1-cells between 1-cells of the underlying bicategory, which form the new objects. Chu-spans may be seen as a… (More)

- Jürgen Koslowski
- 2005

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 present a simple construction of an order-enriched category gam that simultaneously dualizes and parallels the familiar construction of the category rel of relations. Objects of gam are sets, and arrows are games, viewed as special kinds of trees. The quest for identities for the composition of trees naturally leads to the consideration of alternating… (More)

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