GALOIS CONNECTIONS AND CHARACTERIZATION THEOREM FOR DISPERSED, HEREDITARILY DISPERSED, AND HEREDITARY FACTORIZATION STRUCTURES

Abstract

Melton and Strecker have shown that there is a Galois connection between a conglomerate of subcategories of a category and a conglomerate of factorization structures on the category. This Galois connection and the characterization theorem for closed elements in a Galois connection (Theorem 1.3) give us a characterization theorem for the dispersed factorization structures. We “extend” the Galois connection so that it is a Galois connection between a conglomerate of subcategories of a fixed subcategory of Top and a conglomerate of hereditary factorization structures on the fixed subcategory, and we then have a characterization theorem for the hereditarily dispersed factorization structures. We also include a characterization theorem for hereditary factorization structures.