Some categorical properties of Hilbert algebras

Abstract

We show that the category of Hilbert algebras is complete. We also show that it has equalizers, coequalizers and kernel pairs. Coproducts of Hilbert algebras are characterized and finally it is proved that the category of Hilbert algebras is cocomplete.

2000 Mathematics Subject Classification. Primary 18A30; Secondary 18A35.

Key words and phrases. Hilbert algebras, Equalizers, Coequalizers, Limits, Colimits, Kernel pairs, Products and Coproducts, Complete and Cocomplete categories.