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Transactions of the American Mathematical Society

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The Baer sum functor and algebraic $ K$-theory


Author: Irwin S. Pressman
Journal: Trans. Amer. Math. Soc. 162 (1971), 273-286
MSC: Primary 18.10
DOI: https://doi.org/10.1090/S0002-9947-1971-0283048-6
MathSciNet review: 0283048
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Abstract: The Baer sum operation can be described in such a way that it becomes a functorial product on categories of exact sequences of a fixed length. This product is proven to be coherently associative and commutative. The Grothendieck groups and Whitehead groups of some of these categories are computed.


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  • [1] H. Bass, Algebraic K-theory, Benjamin, New York, 1968. MR 40 #2736. MR 0249491 (40:2736)
  • [2] P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer-Verlag, New York, 1967. MR 35 #1019. MR 0210125 (35:1019)
  • [3] P. Hilton, Correspondences and exact squares, Proc. Conference Categorical Algebra (La Jolla, Calif., 1965), Springer, New York, 1966, pp. 254-271. MR 34 #4326. MR 0204487 (34:4326)
  • [4] S. Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #122.
  • [5] -, Natural associativity and commutativity, Rice Univ. Studies 49 (1963), no. 4, 28-46. MR 30 #1160. MR 0170925 (30:1160)
  • [6] -, Categorical algebra, Bull. Amer. Math. Soc. 71 (1965), 40-106. MR 30 #2053. MR 0171826 (30:2053)
  • [7] I. S. Pressman, Functors whose domain is a category of morphisms, Acta Math. 118 (1967), 223-249. MR 35 #4279. MR 0213415 (35:4279)
  • [8] -, Endomorphisms of exact sequences, Bull. Amer. Math. Soc. 77 (1971), 239-242. MR 0268254 (42:3153)
  • [9] -, Whitehead groups of categories of short exact sequences (to appear).
  • [10] N. Yoneda, On Ext and exact sequences, J. Fac. Sci. Univ. Tokyo Sect. I 8 (1960), 507-576. MR 37 #1445. MR 0225854 (37:1445)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0283048-6
Keywords: Algebraic K-theory, Baer sum, category of fractions, coherent functor, counit, unit, Grothendieck group, Whitehead group, short exact sequence, selective abelian category, pullback, pushout
Article copyright: © Copyright 1971 American Mathematical Society

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