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

摘要

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 M used in Part II to give a broad range of applications of chain-valued frames to lattice-valued topology.