Epimorphisms of metric frames

Abstract

This paper deals with several aspects of epimorphisms in the category MFrm of metric frames and contractive homomorphisms. In particular, it is shown that i.

the epicomplete metric frames are uniquely determined by the power-set lattices of sets,

ii.

episurjective is the same as Boolean,

iii.

a metric frame has an epicompletion iff it is spatial, and

iv.

the subcategory of epicomplete L in MFrm is reflective.

Moreover, we show that the counterpart of the latter does not hold for uniform frames.