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CATEGORIES:Category Theory Seminar
SUMMARY:On Varieties of Symmetric Monoidal Closed Categori
es and Dependency of Categorical Diagrams. - Serge
i Soloviev\, IRIT\, Toulouse
DTSTART;TZID=Europe/London:20100617T141500
DTEND;TZID=Europe/London:20100617T151500
UID:TALK25202AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/25202
DESCRIPTION:Do there exist the theories between the axiomatic
theory of Symmetric\nMonoidal Closed Categories (S
MCC) and "fully coherent" partial order? (As\nexa
mples of SMCCs one may take the categories of modu
les over\ncommutative rings with unit.) It turns o
ut that the answer is positive. In\nterms of diagr
ams\, it means that there exist certain non-commut
ative\ndiagrams in free SMCC and certain non-free
SMCC K such that some of these\ndiagrams are alway
s commutative in K while others are not. More rec
ently\,\nit was obtained an infinite series of dia
grams D_n (n\\in N) such that the\ncommutativity o
f D_{n+1} does not imply the commutativity of D_n.
It means\nthat there exist infinitely many interm
ediate theories. This situation is\nradically diff
erent from the well known case of Cartesian Closed
\nCategories. This fact is a strong motivation for
the study of dependency\nof diagrams. Various met
hods of verification of dependency of diagrams are
\ndiscussed. They may be of interest to computer a
lgebra.\n\n(The talk is based on joint work with A
. El Khoury\, L. Mehats\nand M. Spivakovsky.)
LOCATION:MR9\, Centre for Mathematical Sciences
CONTACT:Nathan Bowler
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