NOW MANY INITIAL COMPLETIONS DOES A MONOTOPOLOGICAL CATEGORY HAVE?

Abstract

The initial completions of a monotopological category A in which A is epireflective (called EIC's) are studied via presentations by topological coaxioms in the largest EIC of A, denoted by A_T. It is demonstrated that there is a very close relationship between topological coaxioms satisfied by A and the initial surjections in A, and fence a very close relationship between the latter and the EIC's of A. If A has an EIC which is distinct from A_T, then there exists a largest EIC (denoted by Δ(A)) which is distinct from A_T. An explicit construction of Δ(A) is given. Conditions are found under which A has an EIC distinct from A_T and from its MacNeille completion.