Category theoretic aspects of chain-valued frames: Part I: Categorical and presheaf theoretic foundations

Authors:
A. Pultr;S. E. Rodabaugh
Affiliations:
Department of Applied Mathematics and ITI (Institute of Theoretical Informatics), MFF Charles University, 11800 Praha 1, Czech Republic;Department of Mathematics and Statistics, Youngstown State University, Youngstown, OH 44555-3609, USA
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

This paper is Part I of a two-part series dealing with category theoretic aspects of chain-valued frames. A new categorical motivation for lattice-valued frames is given from presheaves, and then, under the assumption that L be a complete chain, it is established that standard category-theoretic properties (completeness, cocompleteness, factorization structures) hold for L-Frm (the category of L-frames and L-frame morphisms), properties which are a platform for the ''upper'' free functor L and ''lower'' free functor R used in Part II to give a broad range of applications of chain-valued frames to lattice-valued topology.