Limits, standard complexes and $\mathbf{fr}$-codes

S. O. Ivanov   ; R. V. Mikhailov   ; F. Yu. Pavutnitskiy

Sbornik. Mathematics, Tome 211 (2020) no. 11, pp. 1568-1591

Résumé

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.

Détail

Keywords: higher limits, cosimplicial resolutions, cohomological finiteness.

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