Bicohomology theory
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- by Donovan H. Van Osdol PDF
- Trans. Amer. Math. Soc. 183 (1973), 449-476 Request permission
Abstract:
Given a triple T and a cotriple G on a category $\mathcal {D}$ such that T preserves group objects in $\mathcal {D}$, let P and M be in $\mathcal {D}$ with M an abelian group object. Applying the “hom functor” $\mathcal {D}( - , - )$ to the (co)simplicial resolutions ${G^ \ast }P$ and ${T^ \ast }M$ yields a double complex $\mathcal {D}({G^ \ast }P,{T^ \ast }M)$. The nth homology group of this double complex is denoted ${H^n}(P,M)$, and this paper studies ${H^0}$ and ${H^1}$. When $\mathcal {D}$ is the category of bialgebras arising from a triple, cotriple, and mixed distributive law, a complete description of ${H^0}$ and ${H^1}$ is given. The applications include a solution of the singular extension problem for sheaves of algebras.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 183 (1973), 449-476
- MSC: Primary 18H15
- DOI: https://doi.org/10.1090/S0002-9947-1973-0323873-8
- MathSciNet review: 0323873