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Restriction categories II: Partial map classification. (English) Zbl 1023.18005
This paper is a sequel to the same authors’ [J. R. B. Cockett and S. Lack, ibid. 270, 223-259 (2002; Zbl 0988.18003)]. There they introduced restriction categories for working with abstact categories of partial maps, and showed an representation theorem justifying their regarding restriction categories as abstract categories of partial maps. This paper considers when a monad has a Kleisli category which is abstractly a classified category of partial maps. In the presence of products the question has been answered by A. Bucalo, C. Führmann and A. Simpson [ibid. 294, 31-60 (2003; Zbl 1022.18003)]. Moving from the \(p\)-category setting to the restriction category setting, the authors answer the same question without assuming the presence of products.

18C20 Eilenberg-Moore and Kleisli constructions for monads
68Q99 Theory of computing
18B99 Special categories
18D99 Categorical structures
Full Text: DOI
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