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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)

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)

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 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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