A paracyclic (synonym: $\mathbf{Z}$-cyclic) object in a category $C$ is a simplicial object $F_\bullet$ together with a sequence of isomorphisms $t_n : F_n \rightarrow F_n$, $n\geq 1$, such that

where $\partial_i$ are boundaries, $\sigma_i$ are degeneracies. If $t_n^{n+1} = \mathrm{id}:F_n\to F_n$ then the paracyclic object is cyclic.

For example, a paracyclic object in Set is a paracyclic set.

Last revised on April 6, 2018 at 21:54:37. See the history of this page for a list of all contributions to it.