Simplicial complexes are classical objects in combinatorial topology while stellar subdivision and welding are classical operations on them. We present a class of structures whose objects are all simplicial complexes obtained from a given simplicial complex by iterating the subdivision operation and whose morphisms correspond to the welding operation. We prove that this is a projective amalgamation class (projective Fraisse class) and compute its limit and the natural topological quotient of this limit.

The above-described class is hard to handle combinatorially. The difficulty stems from the geometric and multidimensional nature of the objects and morphisms. Consequently, the proof of the amalgamation property is rather unexpected. The high dimensional geometric obstacles are overcome by forming a calculus of finite sequences of finite sets. The proofs are then obtained with combinatorial and calculational methods that rely heavily on the set theoretic nature of the entries of the sequences in the calculus.