Abstract
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.
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Droste, M., Zhang, GQ. (2007). Bifinite Chu Spaces. In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds) Algebra and Coalgebra in Computer Science. CALCO 2007. Lecture Notes in Computer Science, vol 4624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73859-6_13
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DOI: https://doi.org/10.1007/978-3-540-73859-6_13
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