Abstract
We shall prove two theorems on the “triple” cohomology of algebras [1] using a method of acyclic models suggested by H. Appelgate. Specifically, we show that the triple cohomology coincides with slight modifications of the usual theories (the same modifications as used in [8] in the cases of groups and associative algebras). We also prove a direct sum theorem for the cohomology of a coproduct of algebras, subject to a certain condition.
During the preparation of this paper, both authors where partially supported by NSF Contract GP 730.
Received August 26, 1965.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Beck, J.: Triples, algebras and cohomology. To appear.
Eilenberg, S., and S. MacLane: Acyclic models. Amer. J. Math. 75, 189–199 (1953).
— Cohomology theory in abstract groups, I. Ann. Math. 48, 51–78 (1947).
—, and J. C. Moore: Adjoint functors and triples. III. J. Math. 9, 381–398 (1965).
Harrison, D. K.: Commutative algebras and cohomology. Trans. AMS, 104, 191–204 (1962).
Lyndon, R. C.: New proof for a theorem of Eilenberg and MacLane. Ann. Math. 50, 731–735 (1949).
MacLane, S.: Homology. Berlin: Springer 1963.
Barr, M., and G. Rinehart: Cohomology as the derived functor of derivations. To appear in Trans. AIMS.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1966 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Barr, M., Beck, J. (1966). Acyclic Models and Triples. In: Eilenberg, S., Harrison, D.K., MacLane, S., Röhrl, H. (eds) Proceedings of the Conference on Categorical Algebra. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-99902-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-99902-4_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-99904-8
Online ISBN: 978-3-642-99902-4
eBook Packages: Springer Book Archive