nLab abstract circle

Idea

An abstract circle in the sense of (Moerdijk 96) is essentially a cellular structure of the form of a circle $S^1$, in direct analogy to how a linear interval in the abstract sense is a cellular model of the actual topological interval $[0,1]$.

Indeed, just as linear intervals have as classifying topos the category of simplicial sets, so abstract circles have as classifying topos the category of cyclic sets (Moerdijk 96).

References

• Ieke Moerdijk, Cyclic sets as a classifying topos, 1996 (pdf)