  Subobject independence as morphism co-possibility has recently been defined
in [2] and studied in the context of algebraic quantum field theory. This
notion of independence is handy when it comes to systems coming from physics,
but when directly applied to classical algebras, subobject independence is not
entirely satisfactory. The sole purpose of this note is to introduce the notion
of subalgebra independence, which is a slight variation of subobject
independence, yet this modification enables us to connect subalgebra
independence to more traditional notions of independence. Apart from drawing
connections between subalgebra independence and coproducts and congruences, we
mainly illustrate the notion by discussing examples.
