Latent fibrations: fibrations for categories of partial maps. (English) Zbl 1467.18009
Fibrations play a significant role in categorical logic, providing models of type theories [B. Jacobs, Categorical logic and type theory. Amsterdam: Elsevier (1999; Zbl 0911.03001)]. The principal objective in this paper is to develop a theory of fibrations (called latent fibrations) for restriction categories [J. R. B. Cockett and S. Lack, Theor. Comput. Sci. 270, No. 1–2, 223–259 (2002; Zbl 0988.18003); Theor. Comput. Sci. 294, No. 1–2, 61–102 (2003; Zbl 1023.18005); Math. Struct. Comput. Sci. 17, No. 4, 775–817 (2007; Zbl 1123.18003)]. Latent fibrations with various special properties are identified. It is shown that the notion of latent fibration corresponds precisely to the \(2\)-categorical notion introduced in [R. Street, Lect. Notes Math. 420, 104–133 (1974; Zbl 0327.18006)] for the carefully chosen \(2\)-category of restriction semi-functors and restriction transformations.
Reviewer: Hirokazu Nishimura (Tsukuba)
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