Linking the Closure and Orthogonality of Perfect Morphisms in a Category
by
David Holgate
University of Cape Town

In [3] we introduced the pullback closure operator and investigated its application to the theory of perfect morphisms in a category. The present paper refines and extends the main theorem of [3] and aims, through a range of examples, to provide an intuition for the theory developed.

The pullback closure operator is induced by a pointed endofunctor on a category. Such an endofunctor is also used to provide an abstract generalisation of the topological notion of a perfect continuous map - a definition that owes its formulation to a well known result in [2].

Previous studies of perfect morphisms have exploited either the orthogonality or the closure and compactness properties of perfect continuous maps - (cf. [4] and [1]). Our central theorem establishes sufficient criteria on the underlying category and endofunctor to link the orthogonality properties of a perfect morphism with its closure and compactness properties relative to the pullback closure operator.

The examples provided endeavour to justify the choice of sufficient criteria employed in the theorem above.

1 D.Dikranjan, E.Giuli C-perfect morphisms and C-compactness Preprint 1991
2 M.Henriksen, J.R.Isbell Some properties of compactifications Duke Math. Journal 25 1958 83-106
3 D.Holgate The pullback closure operator and generalisations of perfectness Applied Categorical Structures 4 1996
4 G.E.Strecker Perfect sources Proc. Conf. Categorical Topology (Mannheim 1975), Lecture Notes in Mathematics 540 1976 468-500

Date received: June 24, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caah-39.