HeytAlgHeyt Alg is the category whose objects are Heyting algebras and whose morphisms are Heyting algebra homomorphisms, that is lattice homomorphisms which also preserve the Heyting implication. HeytAlgHeyt Alg is a subcategory of Pos.

HetyAlgHety Alg is given by a finitary variety of algebras, or equivalently by a Lawvere theory, so it has all the usual properties of such categories. By general abstract nonsense, the free Heyting algebra on a set XX exists, but it is not easy to describe in general.

category: category

Created on February 1, 2010 18:53:37 by Toby Bartels (