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Journal Articles Fuzzy Sets and Systems Year : 2014

An introduction to quantaloid-enriched categories

Abstract

This survey paper, specifically targeted at a readership of fuzzy logicians and fuzzy set theorists, aims to provide a gentle introduction to the basic notions of quantaloid-enriched category theory. We discuss at length the definitions of quantaloid, quantaloid-enriched category, distributor and functor, always giving several examples that – hopefully – appeal to the intended readership. To indicate the strength of this general theory, we explain in considerable detail how (co)limits are dealt with, and particularly how the Yoneda embedding of a quantaloid-enriched category in its free (co)completion comes to be. Our insistence on quantaloid-enrichment (rather than quantale-enrichment) is duly explained by examples requiring a notion of “partial elements” (sheaves, partial metric spaces). A final section glosses over some further topics, providing ample references for the interested reader.
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Dates and versions

hal-03606895 , version 1 (12-03-2022)

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Isar Stubbe. An introduction to quantaloid-enriched categories. Fuzzy Sets and Systems, 2014, 256, pp.95-116. ⟨10.1016/j.fss.2013.08.009⟩. ⟨hal-03606895⟩
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