Galois Connections and Applications

Galois connections provide the order- or structure-preserving passage between two worlds of our imagination - and thus are inherent in hu­ man thinking wherever logical or mathematical reasoning about cer­ tain hierarchical structures is involved. Order-theoretically, a Galois connection is given simply by two opposite order-inverting (or order­ preserving) maps whose composition yields two closure operations (or one closure and one kernel operation in the order-preserving case). Thus, the "hier