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The inverse Baer\(^*\)-category of a chain. (English) Zbl 1026.18001

Summary: If \((S,\leq)\) is a chain then from \(S\) we construct a category \({\mathcal B}(S)\) with an involution \(*\) together with a canonical embedding \(F: {\mathcal O}rd(S,\leq)\to{\mathcal B}(S)\). We shall show that if \(({\mathcal I},\#)\) is an involution category with \(G: {\mathcal O}rd(S,\leq)\to{\mathcal I}\) an involutive coretraction-valued functor, then there exists a unique involution preserving functor \(H:{\mathcal B}(S)\to{\mathcal I}\) such that \(H\circ F= G\). If \((S,\leq)\) has a least element then \({\mathcal B}(S)\) is an inverse Baer\(^*\)-category.

MSC:

18B35 Preorders, orders, domains and lattices (viewed as categories)
06A05 Total orders
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