An **epicyclic category** is certain small category containing the cyclic category; it has been introduced by Thomas Goodwillie (in an unpublished letter to Waldhausen, August 10, 1987). **Epicyclic sets** ( **epicyclic spaces**) are presheaves of sets (topological spaces, respectively) on the epicyclic category.

- D. Burghelea, Z. Fiedorowicz, W. Gajda,
*Power maps and epicyclic spaces*, J. of Pure and Appl. Algebra**96**:1, pp. 1–14 (Sep 1994) doi - Alain Connes, Caterina Consani,
*Projective geometry in characteristic one and the epicyclic category*, arxiv/1309.0406

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