Organismic Supercategores: II. On Multistable Systems\ud \ud

The representation of biological systems in terms of organismic supercategories, introduced in previous papers by Baianu et al. (Bull. Math. Biophysics,30, 625–636;31, 59–70) is further discussed. To state more clearly this representation some new definitions are introduced. Also, some necessary changes in axiomatics are made. The conclusion is reached that any organismic supercategory has at least one superpushout, and this expresses the fact that biological systems are multistable. This way a connection between some results of Rashevsky’s theory of organismic sets and our results becomes obvious

On Categorical Theory-Building: Beyond the Formal

I propose a notion of theory motivated by Category theory.Comment: 28 pages, no image

Feedback and generalized logic

Although the distinction between software and hardware is a posteriori, there is an a priori distinction that masquerades as the software—hardware distinction. This is the distinction between procedure interconnection, the semantics of flow chart diagrams, which is known to be described by the regular expression calculus; and system interconnection, the semantics of network diagrams, which is described by a certain logical calculus, dual to a calculus of regular expressions. This paper presents a proof of the duality in a special case, and gives the interpretation of the logical calculus for sequential machine interconnection. A minimal realization theorem for feedback systems is proved, which specializes to known open loop minimal realization theorems

Weighted colimits and formal balls in generalized metric spaces

(a) Limits of Cauchy sequences in a (possibly non-symmetric) metric space are shown to be weighted colimits (a notion introduced by Borceux and Kelly, 1975). As a consequence, further insights from enriched category theory are applicable to the theory of metric spaces, thus continuing Lawvere's (1973) approach. Many of the recently proposed d

From axiomatization to generalizatrion of set theory

The thesis examines the philosophical and foundational significance of Cohen's Independence results. A distinction is made between the mathematical and logical analyses of the "set" concept. It is argued that topos theory is the natural generalization of the mathematical theory of sets and is the appropriate foundational response to the problems raised by Cohen's results. The thesis is divided into three parts. The first is a discussion of the relationship between "informal" mathematical theories and their formal axiomatic realizations this relationship being singularly problematic in the case of set theory. The second part deals with the development of the set concept within the mathemtical approach. In particular Skolem's reformulation of Zermlelo's notion of "definite properties". In the third part an account is given of the emergence and development of topos theory. Then the considerations of the first two parts are applied to demonstrate that the shift to topos theory, specifically in its guise of LST (local set theory), is the appropriate next step in the evolution of the concept of set, within the mathematical approach, in the light of the significance of Cohen's Independence results

Weighted colimits and formal balls in generalized metric spaces

(a) Limits of Cauchy sequences in a (possibly non-symmetric) metric space are shown to be weighted colimits (a notion introduced by Borceux and Kelly, 1975). As a consequence, further insights from enriched category theory are applicable to the theory of metric spaces, thus continuing Lawvere's (1973) approach. Many of the recently proposed d