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formal balls of q-categories
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نویسنده
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yang xianbo ,zhang dexue
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منبع
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categories and general algebraic structures with applications - 2023 - دوره : 18 - شماره : 1 - صفحه:1 -18
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چکیده
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The construction of the formal ball model for metric spaces due to edalat and heckmann was generalized to q-categories by kostanek and waszkiewicz, where q is a commutative and unital quantale. this paper concerns the influence of the structure of the quantale q on the connection between yoneda completeness of q-categories and directed completeness of their sets of formal balls. in the case that q is the unit interval [0, 1] equipped with a continuous t-norm &, it is shown that in order that yoneda completeness of each q-category be equivalent to directed completeness of its set of formal balls, a necessary and sufficient condition is that the t-norm & is archimedean.
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کلیدواژه
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q-category ,formal ball ,continuous t-norm ,quantale
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آدرس
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sichuan university, school of mathematics, china, sichuan university, school of mathematics, china
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پست الکترونیکی
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dxzhang@scu.edu.cn
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Authors
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