Co-Universal Algebraic Extension with Hidden Parameters

Abstract

In the research of underlying algebraic structures of real world phenomena, we can find some behavior anomalies
that depend on external parameters that are not ruled by their axiom systems. These are not visible straightaway
and we have to deduce their existence from the eects they cause. To add them in mathematical constructions, we
introduce co-universal extensions of algebras and co-algebras based upon the dual construction of the Kleisli category
associated to a monad.
To illustrate this topic we introduce two applications. The first one is an artificial example. In the second application
we analyze language algebraic structures with a method that states a bridge between language and logic blindly,
that is to say, handling statements through their expressions in those languages satisfying some adequate conditions,
and disregarding their meanings.