Homology, Homotopy and Applications
Volume 15 (2013)
On semisimplicial sets satisfying the Kan condition
Pages: 73 – 82
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.