## Some Fundamental Algebraic Tools for the Semantics of
Computation - Part III: Indexed Categories

**A Tarlecki, R M Burstall and J A Goguen**
*Abstract:* We present the concept of *indexed
category*, a technical tool to model families of categories
defined in a uniform way. We show how any indexed category gives
rise to a single *flat* category, a disjoint union of the
components with some additional morphisms between them. Similarly,
any *indexed functor* (a family of functors between component
categories) induces a flat functor between the corresponding flat
categories. We prove that under some technical conditions flat
categories are complete (resp. cocomplete) if all their components
are so; flat functors have left adjoints if all their components
do. A few examples illustrate the usefulness of these concepts and
results.

*LFCS report ECS-LFCS-88-60*

Previous |

Index |

Next