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math.CT2020
On a simplicial monoid whose underlying simplicial set is not a quasi-category
Ryo Horiuchi
It is well known that the underlying simplicial set of any simplicial group is a Kan complex. Roughly speaking, Kan complex is an infinite-dimensional analogue of groupoid, and the…
math.AT2020
On complicial homotopy monoids
Ryo Horiuchi
For a Kan complex with a vertex, we have the notion of its simplicial homotopy groups. In this paper, for a weak complicial set in the sense of Verity with a vertex, we construct m…