Abstract
Simplicial objects in an arbitrary category C can be described as functors from the category of non-decreasing maps Δ op to C. Similarly one can construct a category, denoted ΔC and called Connes cyclic category, such that a cyclic object in C can be viewed as a functor from ΔC op to C. The cyclic category ΔC was first described by Connes [1983, where it is denoted Λ or ΔK] who showed how it is constructed out of Δ and the finite cyclic groups.
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Loday, JL. (1992). The Cyclic Category, Tor and Ext Interpretation. In: Cyclic Homology. Grundlehren der mathematischen Wissenschaften, vol 301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21739-9_6
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DOI: https://doi.org/10.1007/978-3-662-21739-9_6
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