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Limits, standard complexes and $\mathbf{fr}$-codes
S. O. Ivanova, R. V. Mikhailovab, F. Yu. Pavutnitskiya a Laboratory of Modern Algebra and Applications, Saint Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
Abstract:
For a strongly connected category $\mathscr{C}$ with pairwise coproducts, we introduce a cosimplicial object, which serves as a sort of resolution for computing higher derived functors of $\lim \colon \mathrm{Ab}^{\mathscr{C}}\to \mathrm{Ab}$. Applications involve the Künneth theorem for higher limits and $\lim$-finiteness of $\mathbf{fr}$-codes. A dictionary for the $\mathbf{fr}$-codes with words of length $\leq 3$ is given.
Bibliography: 19 titles.
Keywords:
higher limits, cosimplicial resolutions, cohomological finiteness.
Received: 11.11.2019 and 05.05.2020
Citation:
S. O. Ivanov, R. V. Mikhailov, F. Yu. Pavutnitskiy, “Limits, standard complexes and $\mathbf{fr}$-codes”, Mat. Sb., 211:11 (2020), 72–95; Sb. Math., 211:11 (2020), 1568–1591
Linking options:
https://www.mathnet.ru/eng/sm9348https://doi.org/10.1070/SM9348 https://www.mathnet.ru/eng/sm/v211/i11/p72
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Abstract page: | 832 | Russian version PDF: | 299 | English version PDF: | 34 | References: | 52 | First page: | 118 |
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