References
A. A. Khusainov, “The Hochschild-Mitchell dimension of linearly ordered sets and the continuum hypothesis,” Sibirsk. Mat. Zh.,35, No. 5, 1171–1184 (1994).
B. Mitchell, “Rings with several objects,” Adv. Math.,8, 1–161 (1972).
H. J. Baues and G. Wirsching, “Cohomology of small categories,” J. Pure Appl. Algebra,38, No. 2/3, 187–211 (1985).
S. MacLane, Categories for the Working Mathematician, Springer, New York etc. (1971).
P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory [Russian translation], Mir, Moscow (1971).
S. MacLane, Homology [Russian translation], Mir, Moscow (1966).
A. A. Khusainov, “Cohomology of small categories with coefficients in an abelian category with exact products,” Sibirsk. Mat. Zh.,30, No. 4, 210–215 (1989).
B. Oliver, Higher Limits of Functor on Categories of Elementary Abelianp-Groups Aarhus, 1992. 13 p. (Preprint/Mat. Aarhus Univ.; N 6).
J.-E. Roos, “Sur les foncteurs derives de lim. Applications,” C. R. Acad. Sci. Paris. Sér. I Math. 1961. T. 252, N 24. p. 3702–3704.
D. M. Latch, “The uniqueness of homology for the category of small categories,” J. Pure Appl. Algebra,9, No. 2, 221–237 (1977).
A. A. Khusainov, “The Hochschild-Mitchell dimension of the set of reals is equal to 3,” Sibirsk. Mat. Zh.,34, No. 4, 217–227 (1993).
B. Mitchell, “On the dimension of objects and categories. I. Monoids,” J. Algebra,9, No. 3, 314–340 (1968).
B. V. Novikov, “On partial cohomologies of semigroups,” Semigroup Forum,28, No. 1-3, 355–364 (1984).
B. Mitchell, “A remark on projectives in functor categories,” J. Algebra,69, No. 1, 24–31 (1981).
J. R. Stallings, “On torsion-free groups with infinitely many ends,” Ann. of Math. (2),88, 312–334 (1968).
R. G. Swan, “Groups of cohomological dimension one,” J. Algebra,12, No. 3, 585–601 (1969).
C. C. Cheng and R. Wong, “Hereditary monoid rings,” Amer. J. Math.,104, No. 5, 935–942 (1982).
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The research was supported by the Grant Center for Research in Mathematics at Novosibirsk State University.
Komsomol'sk-na-Amure. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 38, No. 6, pp. 1413–1426, November–December, 1997.
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Khusainov, A.A. Comparing dimensions of a small category. Sib Math J 38, 1230–1240 (1997). https://doi.org/10.1007/BF02675950
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DOI: https://doi.org/10.1007/BF02675950