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Ji r Ad amek and Lurdes Sousa Dedicated to Horst Herrlich with a wish of a nice start into the second half of a good life span
 

Summary: Jir Adamek  and Lurdes Sousa 
Dedicated to Horst Herrlich with a wish of a nice start into the second half of a good life span
Abstract
For each concrete category (K; U) an extension LIM(K;U) is constructed and under certain
\smallness conditions" it is proved that LIM(K;U) is a solid hull of (K; U ), i.e., the least nally
dense solid extension of (K; U ). A full subcategory of Top 2
is presented which does not have
a solid hull.
AMS Subj. Class.: 18A22, 18A30, 18A40, 18B30, 18E15, 54B30.
Key words: Concrete category, MacNeille completion, solid hull, limit closure.
It has been clear from the early development of the theory of concrete categories that the
concept of solid category, introduced by V. Trnkova [21] and R.-E. Ho mann [12], is of major
impact because all \reasonable" concrete categories encountered in algebra and general topology
are solid, and yet, solidness has a number of important consequences. In one respect, however,
solidness is far less satisfactory then other properties (e.g. topological, mono-topological, or
cartesian closed topological): it is the question of solid hulls, i.e., the smallest solid nally dense
extension of a given concrete category. It was Horst Herrlich who started in [9] and [10] a
systematic study of various hulls of concrete categories. Let us recall that in the above three
mentioned cases of topological hull, mono- topological hull and CCT hull a general construction
assigning to a concrete category (K; U) an extension (K  ; U  ) is known, and the basic result is: if

  

Source: Adámek, Jiri - Institut für Theoretische Informatik, Fachbereich Mathematik und Informatik, Technische Universität Braunschweig

 

Collections: Computer Technologies and Information Sciences