{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7JW3EFNJ/4c9116b0-3483-4224-89b1-28aa1130e315/PDF","dcterms:extent":"380 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7JW3EFNJ/514c324f-f92c-43aa-b748-2a1a4b140850/TEXT","dcterms:extent":"0 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-7JW3EFNJ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-OE00UKYR"},{"@xml:lang":"sl","#text":"Matrika"}],"dcterms:issued":"2026","dc:creator":"Ogrin, Dominik","dc:format":[{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"16 str."},{"@xml:lang":"sl","#text":"številka:2"}],"dc:identifier":["ISSN:2385-8567","COBISSID_HOST:291926019","URN:URN:NBN:SI:doc-7JW3EFNJ"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Založba Fakultete za matematiko in fiziko Univerze v Ljubljani"},"dc:subject":[{"@xml:lang":"en","#text":"cohomological lower bound"},{"@xml:lang":"sl","#text":"kohomološka spodnja meja"},{"@xml:lang":"en","#text":"Lusternik-Schnirelmann category"},{"@xml:lang":"sl","#text":"Lusternik-Schnirelmannova kategorija"},{"@xml:lang":"sl","#text":"majhne kategorije"},{"@xml:lang":"en","#text":"small categories"}],"dc:title":{"@xml:lang":"sl","#text":"Cohomological lower bound on the Lusternik-Schnirelmann category of a small category|"},"dc:description":[{"@xml:lang":"sl","#text":"To each topological space ?$X$?, one can assign the least cardinality of an open cover with each member contractible inside ?$X$?. If this cardinality is finite, then the related number is called the Lusternik-Schnirelmann category of ?$X$?. Recently, Kohei Tanaka modified the notion of Lusternik-Schnirelmann category (still a number) so that it is an invariant of (actual) small categories. A classical theorem says that the Lusternik-Schnirelmann category of a topological space can be bounded from below by its cup-length (a number determined by its singular cohomology ring). In the present paper, an analogous result is proved, where ?$X$? is a small category. On the way to this result, an exposition of the nerve construction and cohomology of a small category is given, and the functoriality and “homotopy” invariance of this cohomology are proved"},{"@xml:lang":"sl","#text":"Za topološki prostor ?$X$? se poraja vprašanje: kakšna je najmanjša kardinalnost odprtega pokritja ?$X$?, za katerega velja, da je vsaka odprta množica kontraktibilna znotraj ?$X$?? Kadar je ta kardinalnost končna, se ustrezno število imenuje Lusternik-Schnirelmannova kategorija ?$X$?. Kohei Tanaka je pojem Lusternik-Schnirelmannove kategorije (število) priredil, tako da se aplicira na (dejanske) majhne kategorije. Klasični izrek pravi, da je Lusternik-Schnirelmannovi kategoriji topološkega prostora ?$X$? mogoče postaviti spodnjo mejo - kupa-dolžino (angl. cup-length), definirano preko singularne kohomologije ?$X$?. V pričujočem članku je dokazan analogni izrek, kjer je ?$X$? majhna kategorija. Na poti do tja so predstavljeni pojmi živca, kohomologije majhne kategorije, funktorialnosti in „homotopske“ invariantnosti te kohomološke konstrukcije"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-7JW3EFNJ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-7JW3EFNJ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-7JW3EFNJ/4c9116b0-3483-4224-89b1-28aa1130e315/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza v Ljubljani, Fakulteta za matematiko in fiziko"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-7JW3EFNJ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-7JW3EFNJ"}}}}