Free algebras in varieties

Jan PavlĂ­k

Address: Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic


Abstract: We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to one of equational classes defined by equation arrows. Free algebras in the varieties are investigated and their existence is proved under the assumptions of accessibility.

AMSclassification: primary 08C05; secondary 18C05, 18C20.

Keywords: cocomplete category, free algebra, variety, natural transformation.