AxiomsOfPhysics 2010-06-05 10:32:57 2010-06-05 10:48:20 Topic 1. Seven ideas introduced in the 1963 thesis (1) The category of categories is an accurate and useful framework for algebra, geometry, analysis, and logic, therefore its key features need to be made explicit. (2) The construction of the category whose objects are maps from a value of one given functor to a value of another given functor makes possible an elementary treatment of adjointness free of smallness concerns and also helps to make explicit both the existence theorem for adjoints and the calculation of the specific class of adjoints known as Kan extensions. (3) Algebras (and other structures, models, etc.) are actually functors to a background category from a category which abstractly concentrates the essence of a certain general concept of algebra, and indeed homomorphisms are nothing but natural transformations between such functors. Categories of algebras are very special, and explicit axiomatic characterizations of them can be found, thus providing a general guide to the special features of construction in algebra. (4) The Kan extensions themselves are the key ingredient in the unification of a large class of universal constructions in algebra (as in [Chevalley, 1956]). physics axioms axioms foundations of physics theoretical physics QFT AQFT TQFT General Relativity theory A contributed topic on the Axioms of Physics in the following areas: \begin{enumerate} \item 1. General Relativity Theory \item 2. Axiomatic and Algebraic Quantum Field Theory \item 3. Quantum Algebraic Topology \item 4. Topological Quantum Field Theory \item 5. Quantum Logics \item 6. Symmetry and Physical Principles and Laws \item 7. Categorical Physics: category theory and groupoid/algebraic topology applications in Physics \end{enumerate}