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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 Using th
e general notions of finite presentable and finite
ly generated object introduced by Gabriel and Ulme
r

\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

\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.

\n
\n For more information, contact luca.spada at
gmail.com

\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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