Categorical constructions of Free Algebras, colimits, and completions of partial Algebras

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

Completions of µ-algebras

A μ-algebra is a model of a first order theory that is an extension of the theory of bounded lattices, that comes with pairs of terms (f, μx.f) where μx.f is axiomatized as the least prefixed point of f , whose axioms are equations or equational implications. Standard μ-algebras are complete meaning that their lattice reduct is a complete lattice. We prove that any non trivial quasivariety of μ...

Tree Constructions of Free Continuous Algebras

Topo-canonical completions of closure algebras and Heyting algebras

We introduce and investigate topo-canonical completions of closure algebras and Heyting algebras. We develop a duality theory that is an alternative to Esakia’s duality, describe duals of topo-canonical completions in terms of the Salbany and Banaschewski compactifications, and characterize topo-canonical varieties of closure algebras and Heyting algebras. Consequently, we show that ideal compl...

Limits and Colimits of Hopf Algebras

It is shown that for any commutative unital ring R the category HopfR of R–Hopf algebras is locally presentable and a coreflective subcategory of the category BialgR of R–bialgebras, admitting cofree Hopf algebras over arbitrary R–algebras. The proofs are based on an explicit analysis of the construction of colimits of Hopf algebras, which generalizes an observation of Takeuchi. Essentially be ...