Publication Date

2012-12-05

Availability

Open access

Embargo Period

2012-12-05

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PHD)

Department

Mathematics (Arts and Sciences)

Date of Defense

2012-11-12

First Committee Member

Marvin V. Mielke

Second Committee Member

Shulim Kaliman

Third Committee Member

Victor C. pestien

Fourth Committee Member

Shihab S. Asfour

Abstract

The main purpose of this dissertation is to construct, for various well known families of topological categories and some of their generalizations, a member of the family that is universal in the sense that every member of the family is isomorphic to the pullback, along its so called classifying functor, of the said universal family member. This is carried out by first constructing a topological category that is universal for the family of all topological categories and then by defining various family universal categories by describing their classifying functors. A further refinement is made by placing restrictions on the classifying functors themselves, thus obtaining various "restricted" families of topological categories along with their corresponding "restricted universal categories". These constructions and results are first described in the more general setting of horizontal structures. We will show that all horizontal structures can be obtained by pulling back the universal horizontal structure along an appropriate classifying functor and as a consequence, by restriction, every topological category can be realized as the pullback, along its classifying functor, of the universal topological category.

Keywords

categorical topology, functor

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