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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

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