Homological algebra in topoi
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- by D. H. Van Osdol PDF
- Proc. Amer. Math. Soc. 50 (1975), 52-54 Request permission
Abstract:
Let ${\mathbf {A}}$ be the category of sheaves of universal algebras of some fixed type on a Grothendieck topology. There is defined a cohomology theory ${H^\ast }$ such that if $A$ is an object in ${\mathbf {A}}$ and $M$ is an $A$-module then ${H^1}(A,M)$ is in one-to-one correspondence with the equivalence classes of singular extensions of $A$ by $M$. When ${\mathbf {A}}$ is the category of sheaves of $R$-modules for some sheaf of rings $R$, then ${H^n}(A,M) \cong {\operatorname {Ext} ^n}(A,M)$ for all $n \geq 0$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 52-54
- MSC: Primary 18G99; Secondary 14F20
- DOI: https://doi.org/10.1090/S0002-9939-1975-0369481-1
- MathSciNet review: 0369481