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SUMMARY:On Varieties of Symmetric Monoidal Closed Categories and Dependenc
 y of Categorical Diagrams. - Sergei Soloviev\, IRIT\, Toulouse
DTSTART:20100617T131500Z
DTEND:20100617T141500Z
UID:TALK25202@talks.cam.ac.uk
CONTACT:Nathan Bowler
DESCRIPTION:Do there exist the theories between the axiomatic theory of Sy
 mmetric\nMonoidal Closed Categories (SMCC) and "fully coherent" partial or
 der?  (As\nexamples of SMCCs one may take the categories of modules over\n
 commutative rings with unit.) It turns out that the answer is positive. In
 \nterms of diagrams\, it means that there exist certain non-commutative\nd
 iagrams in free SMCC and certain non-free SMCC K such that some of these\n
 diagrams are always commutative in K while others are not.  More recently\
 ,\nit was obtained an infinite series of diagrams D_n (n\\in N) such that 
 the\ncommutativity of D_{n+1} does not imply the commutativity of D_n. It 
 means\nthat there exist infinitely many intermediate theories. This situat
 ion is\nradically different from the well known case of Cartesian Closed\n
 Categories. This fact is a strong motivation for the study of dependency\n
 of diagrams. Various methods of verification of dependency of diagrams are
 \ndiscussed. They may be of interest to computer algebra.\n\n(The talk is 
 based on joint work with A. El Khoury\, L. Mehats\nand M. Spivakovsky.)
LOCATION:MR9\, Centre for Mathematical Sciences
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