A non-tantalizing approach to tantalic equations
by
Marcel Erné
University of Hannover

A T-semiring or tantale is a complete lattice endowed with a product that distributes over joins and is dominated by the binary meet. The category of T-semirings and join preserving multiplicative homomorphisms is monadic over binary algebras, hence over sets. There exists a nice class of representatives for the epireflections to implicational subcategories, namely the so-called nuclear reflections. These assign to each tantale a nucleus (a special type of closure operation) so that all morphisms become 'continuous'. Under that representation, the equational subcategories correspond to those nuclear reflections which make morphisms 'final'. This provides one more close link between topology and algebra.

Date received: June 6, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeq-40.