## Extending properties to categories of partial maps

**C. Barry Jay**
*Abstract:* Properties can be extended from categories of
total maps to partial maps in a uniform way, e.g. cartesian
products are lifted to *lax* cartesian products.

The partial maps of a category *A* equipped with a dominion
*M* are ordered by their extent of definition, thus forming an
*ordered* category **Ptl**(*A,M*). The **Ptl**
functor preserves adjunctions, including those that define
products, etc. It has a coreflection **Tot** that picks out the
total maps of an arbitrary ordered category, and a reflection
**Dom** which constructs a category of domains for its
morphisms. Each of these adjunctions yields a characterisation of
categories of partial maps, without assuming any further structures
on the categories.

*LFCS report ECS-LFCS-90-107*

Previous |

Index |

Next