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UID:/NewsandEvents/Archives/2013/newsitem/5283/9-O
 ctober-2013-Algebra|Coalgebra-Seminar-Luca-Spada-I
 LLLC-and-University-of-Salerno-
DTSTAMP:20131008T000000
SUMMARY:Algebra|Coalgebra Seminar, Luca Spada (ILL
 LC and University of Salerno)
ATTENDEE;ROLE=Speaker:Luca Spada (ILLLC and Univer
 sity of Salerno)
DTSTART;TZID=Europe/Amsterdam:20131009T160000
DTEND;TZID=Europe/Amsterdam:20131009T180000
LOCATION:ILLC seminar room (F1.15), Science Park 1
 07, Amsterdam
DESCRIPTION:Using the general notions of finite pr
 esentable and finitely generated object introduced
  by Gabriel and Ulmer  in 1971, we prove that, in 
 any category, two sequences of finitely presentabl
 e objects and morphisms (or two sequences of finit
 ely generated objects and monomorphisms) have isom
 orphic colimits (=direct limits) if, and only if, 
 they are confluent. The latter means that the two 
 given sequences can be connected by a back-and-for
 th sequence of morphisms that is cofinal on each s
 ide, and commutes with the sequences at each finit
 e stage. We illustrate  the criterion by applying 
 the abstract results to varieties (=equationally d
 efinable classes) of algebras, and mentioning appl
 ications to non-equational examples.  For more inf
 ormation, contact luca.spada at gmail.com
X-ALT-DESC;FMTTYPE=text/html:\n        <p>Using th
 e general notions of finite presentable and finite
 ly generated object introduced by Gabriel and Ulme
 r<br/>\n        in 1971, we prove that, in any cat
 egory, two sequences of finitely presentable objec
 ts and morphisms (or two sequences of finitely gen
 erated objects and monomorphisms) have isomorphic 
 colimits (=direct limits) if, and only if, they ar
 e confluent. The latter means that the two given s
 equences can be connected by a back-and-forth sequ
 ence of morphisms that is cofinal on each side, an
 d commutes with the sequences at each finite stage
 . We illustrate<br/>\n        the criterion by app
 lying the abstract results to varieties (=equation
 ally definable classes) of algebras, and mentionin
 g applications to non-equational examples.</p>\n  
   \n        <p>For more information, contact <a cl
 ass="email">luca.spada <span class="at">at</span> 
 gmail.com</a></p>\n    
URL:/NewsandEvents/Archives/2013/newsitem/5283/9-O
 ctober-2013-Algebra|Coalgebra-Seminar-Luca-Spada-I
 LLLC-and-University-of-Salerno-
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