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Mat. Sb., 2020, Volume 211, Number 11, Pages 72–95 (Mi msb9348)  

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.

Funding Agency Grant Number
Russian Science Foundation 16-11-10073
Ministry of Education and Science of the Russian Federation 14.W03.31.0030
The main results of this work (Theorem 2 and the results in § 5) were obtained with the support of the Russian Science Foundation under grant no. 16-11-10073. This research was also supported by a grant for State Support of Scientific Research Conducted under the Auspices of Leading Scientists of the Government of the Russian Federation (project no. 14.W03.31.0030).

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9348

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English version:
Sbornik: Mathematics, 2020, 211:11, 1568–1591

Bibliographic databases:

UDC: 512.664
MSC: Primary 18A30; Secondary 18G10, 20J05
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

Citation in format AMSBIB
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\pages 72--95
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