Domains and lambda-calculi
Domains for Denotational Semantics
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Chu spaces as a semantic bridge between linear logic and mathematics
Theoretical Computer Science - Linear logic
The Stone Gamut: A Coordinatization of Mathematics
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Full Completeness of the Multiplicative Linear Logic of Chu Spaces
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Higher dimensional automata revisited
Mathematical Structures in Computer Science
A Categorical View on Algebraic Lattices in Formal Concept Analysis
Fundamenta Informaticae
A Monoidal Category of Bifinite Chu Spaces
Electronic Notes in Theoretical Computer Science (ENTCS)
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
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This paper studies colimits of sequences of finite Chu spaces and their ramifications. We consider three base categories of Chu spaces: the generic Chu spaces (C), the extensional Chu spaces (E), and the biextensional Chu spaces (B). The main results are: (1) a characterization of monics in each of the three categories; (2) existence (or the lack thereof) of colimits and a characterization of finite objects in each of the corresponding categories using monomorphisms/injections (denoted as iC, iE, and iB, respectively); (3) a formulation of bifinite Chu spaces with respect to iC; (4) the existence of universal, homogeneous Chu spaces in this category. Unanticipated results driving this development include the fact that: (a) in C, a morphism (f, g) is monic iff f is injective and g is surjective while for E and B, (f, g) is monic iff f is injective (but g is not necessarily surjective); (b) while colimits always exist in iE, it is not the case for iC and iB; (c) not all finite Chu spaces (considered set-theoretically) are finite objects in their categories. This study opens up opportunities for further investigations into recursively defined Chu spaces, as well as constructive models of linear logic.