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Identities in Categories

Published online by Cambridge University Press:  20 November 2018

H. Herrlich  and
C. M. Ringel
H. Herrlich
Affiliation:
Mathematisches Institut der Universitât, D. 48, Bielefeld, Germany
C. M. Ringel
Affiliation:
Carleton University, Ottawa, Ontario
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In [4] Hatcher introduced the notion of an identity in an arbitrary category and proved a characterization of quasivarietal subcategories which is similar to Birkhoff's characterization of varietal subcategories in universal algebra. The aim of this note is to show that the theorem of Hatcher as well as the categorical generalization of Birkhoff's theorem are special cases of a "relative" theorem, formulated with respect to a projective structure.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 297 - 299
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Birkhoff, G., On the structure of abstract algebras, Proc. Cambridg. Philos. Soc. 31 (1935), 433-454.Google Scholar
2. Eilenberg, S. and Moore, J. C., Foundation of relative homological algebra, Memoir. Amer. Math. Soc. 55, 1965.Google Scholar
3. Felscher, W., Kennzeichnung von primitiven und quasiprimitiven Kategorien von Algèbren, Arch. Math. 19 (1968), 390-397.Google Scholar
4. Hatcher, W. S., Quasiprimitive subcategories, Math. Ann. 190 (1970), 93-96.Google Scholar
5. Herrlich, H., Algebraic categories, An axiomatic approach, Manuscript.Google Scholar
6. Isbell, J. R., Normal completions of categories, Reports of the Midwest Category Seminar. Lecture Notes 47 (1967), 110-155.Google Scholar
7. Lawvere, F. W., Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 869-872.Google Scholar
8. Linton, F. E. J., Some aspects ofequational categories, Proc. Conf. categ. algebra, La Jolla, 1965; Berlin (1966), 84-94.Google Scholar
9. Malcev, A., On the general theory of algebraic systems (Russian), Mat. Sb. 35 (1954), 3-20.Google Scholar
10. Maranda, J., Injective structures, Trans. Amer. Math. Soc. 110 (1964), 98-135.Google Scholar