Limits, standard complexes and fr-codes

Abstract

For a strongly connected category $\mathcal{C}$ with pair-wise coproducts, we introduce a cosimplicial object, which serves as a sort of resolution for computing higher derived functors of $\mathsf{lim}:{\mathrm{Ab}}^{\mathcal{C}}\to \mathrm{Ab}$. Applications involve Künneth theorem for higher limits and $\mathsf{lim}$-finiteness of $\mathbf{fr}$-codes. A dictionary for the $\mathbf{fr}$-codes with words of length $\le 3$ is given.

23 pages