Nikica Uglešić*
University of Zadar, Croatia
University of Zadar, Croatia
For every category pair, such that the subcategory is dense (in the
sense of expansions) and full, an (abstract) weak shape category is
constructed. The key technical notions are a hyperladder and a certain
homotopy relation which induce a weak shape morphism. There exists a
faithful functor of the shape category to the weak shape category, and
there exists a pair of continua having the same weak shape type and
different shape types. Several important well known shape invariants
(connectedness, trivial shape, shape dimension < n, movability, Mittag-Leffler property, strong movability) are, actually, weak shape invariant
properties.
* This is a joint work with Branko Červar.
