Graphic toposes, n-categories and resulting problems of computer algebra
Date: July 18th (Thursday)
Time: 16:45-15:30
Abstract
In 1989 I proposed pre-sheaves of a special kind as algebraic, displayable
descriptions of hierarchical systems. The multi- dimensional graphs underlying
n-categories (i.e.ball-and- hemisphere complexes) form a central example, but finite
monoids satisfying the identity xyx = xy play the pivotal role. New algebraic results
involving these toposes include an intimate connection with Coxeter groups and a
characterization of the commonly-occuring case in which the lattice of sub-toposes is a
total order. Computer graphics should be capable of displaying the geometric realizations of
these objects as computer algebra should be capable of solving the relevant word problems
for a known graphic monoid. Whether more than a few such monoids are needed to govern
the modeling of the access-algebra of HYPERTEXT or similar hierarchies remains to be
seen.
