Keywords
- Abelian Group
- Exact Sequence
- Natural System
- Homotopy Class
- Linear Extension
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References
Baues, H.J.: Algebraic homotopy, appears in Cambridge University Press.
Baues, H.J.: The homotopy types of 4-dimensional CW-complexes, Preprint. MPI. Bonn. 1986.
Baues, H.J. and Wirsching, G.: The cohomology of small categories, J. Pure and Appl. Alg. 38, 1985, 187–211.
Bousfield, A.K. and Kan, D.M.: Homotopy limits, Completions and localization, Lect. Notes Math. 304, 1972.
Cartan, H. and Eilenberg, S.: Homological Algebra, Princeton University Press, 1956.
Curtis, E.B.: Some relations between homotopy and homology. Ann. of Math. 83, 1965, 386–413.
Datuashvili, T.: On cohomology of small categories. Proc. Mat. Institut Tbilisi, 62, 1979, 28–37. /Russian/.
Dold, A. and Puppe, D.: Homologie nicht-additivez Functoren. Anwendungen, Ann. Inst. Fourier, 11, 1961, 201–312.
Holt, O.F.: An interpretation of the cohomology groups Hn(G,M). J. Algebra, 60, 1979, 307–318.
Huebschmann, J.: Crossed n-fold extensions of groups and cohomolgy. Comm. math. Helv. 55, 1980, 302–314.
Inasaridze, H.: Some aspects of homological and homotopical algebra and its applications. Proc. math. inst. Tbilisi 48, 1975, 1–140. /Russian/.
Jibladze, M. and Pirashvili, T.: On some linear extension of the category of finitely generated free modules. Bull. Ac. Sc. Georgian SSR, 123, 3, 1986, 481–484. /Russian/.
Jibladze, M. and Pirashvili, T.: Cohomology of algebraic theories /to appear/.
Loday, J.L.: Cohomologie et groupe de Steinberg relatifs. J. Algebra, 54, 1978, 178–202.
Loday, J.L.: Spaces with finitely many nontrivial homotopy groups. J. Pure and Appl. Algebra, 24, 1982, 179–202.
May, J.P.: Simplicial objects in Algebraic Topology. Princeton: Van Nostrand, 1967.
Pirashvili, T.: Cohomology of small categories and models for homotopy theories. Bull. Ac. Sc. Georgian SSR, 129, 2, 1988, 261–264 /Russian/.
Quillen, D.: Homotopical algebra. Lect. Notes Math. 43, 1967.
Quillen, D.: Higher algebraic K-theory I, Lect. Notes Math. 341, 1973, 85–147.
Schubert, H.: Kategorien. Bd. II. Springer. Berlin. 1970.
Unsöld, H.M.: On classification of spaces with free homology. Freien Universität Berlin, 1987.
Witt,E.: Treue Darstellung Liescher Ring. J. reine und angew. Math. 177, 152–160.
Whitehead, J.H.C.: Certain exact sequence. Ann. Math. 52, 1950, 51–110.
Yoneda, N.: On Ext and Exact sequences. J.Fac.Sci.Tokyo.Sec.I. 1960, V.8, 507–526.
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Pirashvili, T. (1990). Cohomology of small categories in homotopical algebra. In: Inassaridze, H. (eds) K-theory and Homological Algebra. Lecture Notes in Mathematics, vol 1437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086724
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