Categorical Computing Systems
Keywords:
computing, category, toposAbstract
This paper is the second (first see [1]) in a series whose goal is to develop a fundamentally new way of constructing theories of cacomputing (categorical computing). The motivation comes from a desire to address certain deep issues that arise when contemplating quantum and mathematical biology’s’ theories of space and time. A topos is special type of the category. The topos approach to the formulation of informatics’ theories includes a new form of informatics’ logic. We present this topos informatics’ logic, including some new results, and compare it to standard intuitionistic logic, all with an eye to conceptual issues. Importantly, topos informatics’ logic comes with a clear geometrical underpinning.
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