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Revision Browser : Axioms of Physics
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view 'Axioms of Physics
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2010-10-31 20:30:24
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Version = 9
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bci1
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\begin{thebibliography}{99}
\bibitem{IN1}
Isaac Newton. 1686.\emph{Principles of Natural
Philosophy}.
\bibitem{IN2}
``Works of Sir Isaac Newton--Isaaci Newtoni Opera
quae exstant omnia"
\bibitem{AE1}
Albert Einstein. 1956. \emph{Relativity Theory}. NL
\bibitem{IN2}
Dirac, Paul A.M. 1958. \emph{Principles of Quantum
Mechanics}. NL
\bibitem{IN2}
Richard Feynman. 1965. \emph{Lecture Notes in
Physics}. NL
\bibitem{IN2}
Stephen Weinberg. 1994. \emph{Quantum FieldTheory}.
NL
\bibitem{ESKGM65}
Eilenberg, S., and Kelly, G.M., Closed Categories,
\emph{Proceedings of the Conference on Categorical
Algebra} (La Jolla 1965), Springer Verlag 1966.
\bibitem{ESML45}
Eilenberg, S., and Mac Lane, S., General Theory of
Natural Equivalences, \emph{Trans. Amer. Math.
Soc.} 58, 231--294 (1945).
\bibitem{KDM1}
Kan, D. M., Adjoint Functors, Trans. Amer. Math.
Soc. 87, 294--329 (1958).
Lawvere, F. W., Functorial Semantics of Algebraic
Theories, Proc. Nat. Acad. Sc. U.S.A. 50, 869--872
(1963).
\bibitem{LFW66}
Lawvere, F. W., The Category of Categories as a
Foundation for Mathematics, Proceedings of the
Conference on Categorical Algebra (La Jolla 1965),
Springer Verlag. 1966
(See also the Review 7332 by J. Isbell, Dec. 1967,
Math. Reviews).
\bibitem{LMS65}
Mac Lane, S., Categorical Algebra,
\emph{Bull. Amer. Math. Soc.}, 71, 40--106 (1965).
\end{thebibliography}
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2010-06-05 11:44:37
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Version = 5
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Version 6
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bci1
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Bibliography
Eilenberg, S., and Kelly, G.M., Closed Categories, Proceedings of the Conference on Categorical
Algebra (La Jolla 1965), Springer Verlag 1966.
Eilenberg, S., and Mac Lane, S., General Theory of Natural Equivalences, Trans. Amer.
Math. Soc. 58, 231–294 (1945).
Kan, D. M., Adjoint Functors, Trans. Amer. Math. Soc. 87, 294–329 (1958).
Lawvere, F. W., Functorial Semantics of Algebraic Theories, Proc. Nat. Acad. Sc. U.S.A. 50,
869–872 (1963).
Lawvere, F. W., The Category of Categories as a Foundation for Mathematics, Proceedings
of the Conference on Categorical Algebra (La Jolla 1965), Springer Verlag 1966 [See also
Review 7332 by J. Isbell, Dec. 1967, Math. Reviews].
Mac Lane, S., Categorical Algebra, Bull. Amer. Math. Soc. 71, 40–106 (1965).
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2010-06-05 10:48:34
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Version = 2
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Version 3
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bci1
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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]).
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