Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372055
Title: Quantales : Quantal sets.
Author: Nawaz, M.
Awarding Body: University of Sussex
Current Institution: University of Sussex
Date of Award: 1985
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Abstract:
A generalisation of Q-sets (and maps between them) called quantal sets, is introduced for an idempotent quantale Q. It turns out that subsets of a quantal set do not correspond bijectively with its subobjects. Quantal sets are shown to form a topos with an internal quantale which classifies subsets. We define appropriate notions of complete quantal set, presheaf and sheaf over Q, and show that the categories of quantal sets and sheaves over Q are equivalent. Based on subsets of quantal sets, a category is constructed in which the properties of the &-operation of Q are reflected. Finally, we construct a bicategory m from Q, and define a concept of quasi-symmetric E-category; it is proved that complete quantal sets may be characterised as quasi-symmetric E-categories satisfying additional properties.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.372055  DOI: Not available
Keywords: Categorical algebra Mathematics
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