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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Coalgebras, sheaves, and cohomology

Author: D. H. Van Osdol
Journal: Proc. Amer. Math. Soc. 33 (1972), 257-263
MSC: Primary 18C15
MathSciNet review: 0294447
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Abstract: The category of sheaves on the topological space X with values in the algebraic category $ \mathcal{A}$ is shown to be cotripleable under the stalk category $ {\mathcal{A}^{\vert X\vert}}$. If K is a field then the category of K-coalgebras is shown to be cotripleable under the category of K-vector spaces. This makes possible the interpretation of the first group of the associated triple cohomology complex. In particular, for coalgebras our $ {H^1}$ is isomorphic to Jonah's $ {H^2}$.

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Keywords: Sheaves of algebras, cotripleable, coalgebras, principal objects, cogroup object, extension, Jonah cohomology
Article copyright: © Copyright 1972 American Mathematical Society