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Topological balls. (English) Zbl 0922.18004
The so-called Chu-construction was introduced in 1979 by P.-H. Chu in the appendix to his supervisor M. Barr’s book [“$$*$$-autonomous categories”, Lect. Notes Math. 752 (1979; Zbl 0415.18008)] for the purpose of constructing symmetric $$*$$-autonomous categories out of symmetric monoidal closed ones and a specified object. Regarded as a curiosity for some time, it recently has been the object of renewed interest, e.g., by M. Barr himself [J. Pure Appl. Algebra 111, No. 1-3, 1-20 (1996; Zbl 0857.18010) and Theory Appl. Categ. 2, No. 2, 17-35 (1996; Zbl 0857.18009)], V. Pratt and E. Schläpfer [Doctoral Thesis, Faculty of Science, Université de Fribourg (1998)]. Certain ad hoc constructions of (symmetric) $$*$$-autonomous categories nowadays can be better understood (and sometimes simplified) when viewed in terms of the Chu-construction and its refinements. A case in point is the category of reflexive $$\zeta$$-$$\zeta^{\ast}$$-balls. It was introduced by M. Barr [Cah. Topologie Géom. Différ. 17, 335-342 (1976; Zbl 0344.46132)] and his 1979 book and is revisited here from the new perspective.

MSC:
 18B99 Special categories 46B99 Normed linear spaces and Banach spaces; Banach lattices 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
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References:
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