Geodesic
Algebraic Deformations and Bicohomology
Canadian mathematical bulletin, Tome 32 (1989) no. 2, pp. 182-189

Voir la notice de l'article provenant de la source Cambridge University Press

Recently we have introduced an enriched cohomology theory for categories that are tripleable (algebraic) over a category of modules. The cohomology admits a circle product, related to the obstruction problem for algebraic deformations, making the total complex a graded ring. We here offer similar constructions in two other situations - coalgebraic and bialgebraic categories. Examples include categories of bialgebras, sheaves of modules, and sheaves of algebras over a sheaf of rings.
DOI : 10.4153/CMB-1989-027-9
Mots-clés : 18C15, 18G99, 16A58 
Fox, Thomas F. Algebraic Deformations and Bicohomology. Canadian mathematical bulletin, Tome 32 (1989) no. 2, pp. 182-189. doi: 10.4153/CMB-1989-027-9
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[1] 1. Barr, M. and Beck, J., Homology and standard constructions, Lecture Notes in Math. Vol. 80, Springer-Verlag, Berlin and New York, 1969, 245–334. Google Scholar

[2] 2. Beck, J., Triples, algebras and cohomology, Dissertation, Columbia University, New York, 1967. Google Scholar

[3] 3. Distributive laws, Lecture Notes in Math. Vol. 80, Springer-Verlag, Berlin and New York, 1969, 119–140. Google Scholar

[4] 4. Doi, Y., Homological coalgebra, J. Math. Soc. Japan 33(1981), 31-50 5. S. Eilenberg and Moore, J. C., Homology and fibrations I; coalgebras, cotensor product and its derived functors, Comm. Math. Helv. 40 (1966), 199-236. Google Scholar

[6] 6. Fox, T. F., Algebraic deformations and triple cohomology, Proc. Amer. Math. Soc. 78 (1980), 467-472. Google Scholar

[7] 7. The coalgebra enrichment of algebraic categories, Comm. Algebra 9 (1981), 223-234. Google Scholar

[8] 8. Operations on triple cohomology, J. Pure Appl. Algebra 51 (1988), 119-128. Google Scholar

[9] 9. Gerstenhaber, M., On the deformation of rings and algebras, Ann. Math. (2) 79 (1964), 59-103. Google Scholar

[10] 10. On the deformation of sheaves of rings, in “Global Analysis, Papers in Honor of K. Kodaira”, Spencer, D. C. and Iyanaga, S. (eds.), Tokyo and Princeton U. presses, 1969. Google Scholar

[11] 11. Kleiner, M., Integrations and cohomology in the Eilenberg-Moore category of a monad, preprint (1986). Google Scholar

[12] 12. Jonah, D. W., “Cohomology of Coalgebras”, Mem. Amer. Math. Soc. Vol. 82, 1968. Google Scholar

[13] 13. MacLane, S., “Homology. Springer-Verlag, Berlin, 1963. Google Scholar

[14] 14. Van Osdol, D. H., Coalgebras, sheaves, and cohomology, Proc. Amer. Math. Soc. 33 (1972), 257– 263. Google Scholar

[15] 15. Bicohomology theory, Trans. Amer. Math. Soc. 183 (1973), 449–476. Google Scholar

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