KGTA seminar, 30. januar 2018.

Naredni sastanak Seminara biće održan u utorak, 30. januara 2018, u sali 844 Matematičkog fakulteta sa početkom u 14 časova.

Predavač: Branko Nikolić, Macquarie University, Sydney

Naslov predavanja: METRIC AND (RELATIVISTIC) CAUSAL SPACES VIA ENRICHMENT

Apstrakt: We give a short introduction to basics of (enriched) category theory. When the base of enrichment is a monoidal category that is in fact a poset (aka quantale), the definition of an enriched category becomes simpler. We consider two particular quantales consisting of positive real numbers. Categories enriched in the first are generalized metric spaces [1]. The categories enriched in the second can be interpreted as causal preorders that remember intervals (times) between time-like events [2]. Modules between enriched categories enable expressing Cauchy completeness of metric spaces in purely categorical terms; in this sense all event spaces are Cauchy complete. We give sufficient conditions on a monoidal category that ensure that an enriched category is Cauchy complete if and only if idempotents split in its underlying category.

[1] Lawvere, F. W. Metric spaces, generalized logic, and closed categories. Rendiconti del Seminario Matematico e Fisico di Milano 43, 1 (1973), 135–166.
[2] Nikolić, B. Cauchy completeness and causal spaces. arXiv:1712.00560v1 [math.CT] (2017)



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