Mathematica Pannonica CARTESIAN CLOSEDNESS IN CAT EGORIES OF PARTIAL ALGEBRAS

We study categories of partial algebras of the same type In these categories we de ne a binary operation of exponentiation for objects and investigate its behaviour We discover two cartesian closed initially structured subcategories in every category of partial algebras of the same type It is well known that concrete categories having well behaved func tion spaces i e being initially structured and cartesian closed play an important role in applications to many branches of mathematics It is therefore worthwhile to look for such categories also among categories of general algebraic systems In this note we focus our interest onto categories of partial algebras As for generality partial algebras lie be tween total i e universal algebras and relational systems Therefore when studying partial algebras we can extend considerations known for total algebras or restrict those known for relational systems However such an extension or restriction is often not quite trivial and many new particular considerations have to be done for partial algebras This research was supported by Grant Agency of the Czech Republic grant no