abstract circle

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).

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

Created on March 31, 2014 at 00:18:34. See the history of this page for a list of all contributions to it.