Homology, Homotopy and Applications

Volume 15 (2013)

Number 1

On semisimplicial sets satisfying the Kan condition

Pages: 73 – 82

DOI: https://dx.doi.org/10.4310/HHA.2013.v15.n1.a4


James E. McClure (Department of Mathematics, Purdue University, West Lafayette, Indiana, U.S.A.)


A semisimplicial set has face maps but not degeneracies. A basic fact, due to Rourke and Sanderson, is that a semisimplicial set satisfying the Kan condition can be given a simplicial structure. The present paper gives a combinatorial proof of this fact and a generalization to multisemisimplicial sets.


semisimplicial set, Kan condition

2010 Mathematics Subject Classification

Primary 55P43. Secondary 57P10, 57R67.

Published 1 May 2013