 One also can consider the problem of the status of the Common Cause Principle in discrete (lattice) quantum field theory. This is a simplified model of quantum field theory in which calculations are frequently easier to carry out. One of the simplifications of this theory is that the algebras of local observables are finite dimensional. The quantum probability spaces determined by such observables are not purely non-atomic and this prevents common causes—localized or not—to exist in these theories (Hofer-Szabó &amp; Vecsernyés 2012a). If, in the quantum context, one allows common causes not to commute with the correlated observables, then “non-commutative” common causes can be shown to exist in lattice quantum field theory (Hofer-Szabó &amp; Vecsernyés 2012b, 2013, 2018). One also can raise the problem of the status of the Common Cause Principle in categorial quantum field theory (Brunetti, Fredenhagen, &amp; Verch 2003; Rédei 2014a). This requires a reformulation of the concept of common cause in terms of the notions of the categories used in categorial quantum field theory, which is done in Rédei (2014a). This then leads to a number of specific questions about the status of the suitable reformulated Common Cause Principle. Most of these questions are open—this is an active area of research.