An impossibility theorem demonstrates that a particular problem or set of problems cannot
be solved as described in the claim. Such theorems put limits on what is possible to do …

Advanced undergraduate or beginning graduate students need a unified foundation for their
study of geometry, analysis, and algebra. For the first time, this book uses categorical …

After an introductory section, this article will focus on four questions: How should the Kyoto
School be defined? What is meant by its central philosophical concept of “absolute …

We present a method for providing semantic interpretations for languages with a type system
featuring inheritance polymorphism. Our approach is illustrated on an extension of the …

From a Geometrical Point of View explores historical and philosophical aspects of category
theory, trying therewith to expose its significance in the mathematical landscape. The main …

General structure of metabolism includes the reproduction of catalysts that govern
metabolism. In this structure, the system becomes autopoietic in the sense of Maturana and …

" In this book, it is argued that the notorious logical paradoxes-the Liar, Russell's, the Sorites-
are only the noisiest of many. Contradictions arise in the everyday, from the smallest points …

Following F. William Lawvere, we show that many self-referential paradoxes,
incompleteness theorems and fixed point theorems fall out of the same simple scheme. We …

We apply some tools developed in categorical logic to give an abstract description of
constructions used to formalize constructive mathematics in foundations based on …

Most of the present material was first presented at the Battelle Institute Conference on
Category Theory in 1968, but was not included in the proceedings of that conference. While …