Abramsky S, Blute R, Panangaden P, Nuclear and Trace Ideals in Tensored *- Categories, to appear in: Journal of Pure and Applied Algebra. Home/Search Document Details and Download
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Categories of Circuits - Katis, Sabadini, Walters, Weld (1999) (Correct)
....have received some attention in theoretical computer science. For instance, they feature in the following papers: 1] and [2] on game semantics and Interaction Categories; 11] on cyclic structures and recursive computation; 14] on premonoidal categories, and mixed data and control ow graphs; [3] on nuclear and trace ideals, and probabilistic relations ; 4] on linearly distributive categories; 15] and [5] on relational models of circuit design ; and [27] on the semantics of asynchronous communication in networks of parallel processes. This paper is part of a project ( 24] 9] 23] ....
....ne a traced monoidal category BinCirc of binary circuits. We then de ne a subcategory DOBC of determined output binary circuits and, further, a subcategory ABC DOBC of asynchronous binary circuits. 12 These last two categories only admit a partially de ned feedback operation; in the language of [3], these categories admit trace ideals a notion recalled in Section 4.2. The category of asynchronous binary circuits is shown to be generated (as a symmetric monoidal category with a trace ideal) by instantaneous circuits computing functions and the inertial binary delay (Proposition 4 and ....
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Abramsky S, Blute R, Panangaden P, Nuclear and Trace Ideals in Tensored *- Categories, to appear in: Journal of Pure and Applied Algebra.
Higher-Order and Reflexive Action Calculi: Their Type Theory .. - Gardner, Hasegawa (1998) (Correct)
.... balanced monoidal categories (monoidal categories with braiding and twisting) for our purpose we only need the case of symmetric monoidal categories as presented in [Has97a, Has97b] Further discussions and applications of traced monoidal categories in the context of computer science are found in [Abr96, ABP98, BCS98]. As a precursor we note that Cazanescu and S tefanescu had the notion of biflows in mid 80s [CS88] whose axiomatization is equivalent to that of traced symmetric monoidal categories; see also [Mil94b] for historical remarks on related concepts. Definition 4.13 A symmetric monoidal category C ....
Abramsky, S., Blute, R., and Panangaden, P. (1998), Nuclear and trace ideals in tensored *-categories, Manuscript.
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