A finite simplicial set is a simplicial set having only a finite number of non degenerate simplicies. It is not hard to show that every finite simplicial set has only a finite number of simplicies in each degree. My question is: does the converse hold? that is, is every simplicial set, having a finite number of simplicies in each degree, necessarily finite?



Finite simplicial sets
Let G be a finite group viewed as a one object category. Then the nerve BG is a simplicial set with finitely many simplices in each dimension but it is not finite.


