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Abstract
Several fundamental problems are discussed concerning general systems. First, the type function is defined, and the surjectivity of type functions is shown. Second, the cardinal and ordinal functions of general systems are defined, and the surjectivity of the order function and the object set cardinal function is proved. For the concepts of homomorphisms and isomorphisms of systems, it is shown that the set of homomorphisms and the set of isomorphisms of algebras are the same as the set of homomorphisms and the set of isomorphisms of systems, induced by the algebras, respectively. The paper concludes with a study of the existence of the category of general systems and the existence of the functor induced by algebras.