EQUALIZERS IN THE CATEGORIES FUZZ AND TOPFUZZ

Abstract

It is well known that the categories Fuzz of fuzzes and TopFuzz<br /> of topological fuzzes are both complete and cocomplete, and some categorical<br /> properties of them were introduced by many authors. In this paper, we introduce<br /> the structure of equalizers in these categories. In particular, we show that every<br /> regular monomorphism is an injective map, but monomorphisms need not be<br /> injective, in general.