## Journal of Symbolic Logic

### An algebraic approach to categories of partial morphisms

S. T. Stefani

#### 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.

#### Article information

Source
J. Symbolic Logic, Volume 67, Issue 1 (2002), 117-129.

Dates
First available in Project Euclid: 18 September 2007

https://projecteuclid.org/euclid.jsl/1190150033

Digital Object Identifier
doi:10.2178/jsl/1190150033

Mathematical Reviews number (MathSciNet)
MR1889540

Zentralblatt MATH identifier
1001.18002

Subjects
Primary: 18B99: None of the above, but in this section

#### Citation

Stefani, S. T. An algebraic approach to categories of partial morphisms. J. Symbolic Logic 67 (2002), no. 1, 117--129. doi:10.2178/jsl/1190150033. https://projecteuclid.org/euclid.jsl/1190150033