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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Extension of algebraic theories


Authors: E. James Peake and Galen R. Peters
Journal: Proc. Amer. Math. Soc. 32 (1972), 358-362
MSC: Primary 18A99; Secondary 08A25
MathSciNet review: 0299651
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Abstract: The algebraic theories of Lawvere are extended in a natural way to small complete categories. These categories exhibit not only the operations and identities, but some of the homomorphisms, functions, objects and constructions which are encountered when working within the algebraic categories associated with the theories. The category of extended theories is isomorphic to the original category of theories. As an illustration, the extended theory of groups is used to construct commutator subgroups.


References [Enhancements On Off] (What's this?)

  • [1] F. W. Lawvere, Functorial semantics of algebraic theories, Unpublished Ph.D. Thesis, Columbia University, New York, 1963.
  • [2] F. William Lawvere, Some algebraic problems in the context of functorial semantics of algebraic theories, Reports of the Midwest Category Seminar. II, Springer, Berlin, 1968, pp. 41–61. MR 0231882
  • [3] S. Mac Lane, Categorical algebra, National Science Foundation Advanced Science Seminar, Bowdoin College, Mathematics Dept., Brunswick, Maine, 1969.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0299651-X
Keywords: Algebraic theory, structure, semantics, algebraic category
Article copyright: © Copyright 1972 American Mathematical Society