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An algebraic approach to categories of partial morphisms

Published online by Cambridge University Press:  12 March 2014

S. T. Stefani
S. T. Stefani*
Affiliation:
Facoltà Di Scienze M. F. N., Università Di Venezia, Venezia, Italy, E-mail: [email protected]
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Abstract

In the study of categories whose morphisms display a behaviour similar to that of partial functions, the concept of morphism domain is, obviously, central. In this paper an operation defined on morphisms describes those properties which are related to morphisms being regarded as abstractions of partial functions. This operation allows us to characterise the morphism domains directly, and gives rise to an algebra defined by a simple set of identities. No product-like categorical structures are needed therefore. We also develop the construction of topologies together with the notion of continuous morphism, in order to test the effectiveness of this approach. It is interesting to see how much of the computational character of the morphisms is translated into continuity.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 1 , March 2002 , pp. 117 - 129
Copyright
Copyright © Association for Symbolic Logic 2002

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References

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