Abstract:In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category {Set} of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.
Keywords: concrete category, optimal subset, reflexive subobject lattice, reflexive endomorphism algebra
AMS Subject Classification: Primary 46C10, 47C05, 06A35