  We develop a theory of limits for sequences of dense abstract simplicial
complexes, where a sequence is considered convergent if its homomorphism
densities converge. The limiting objects are represented by stacks of
measurable [0,1]-valued functions on unit cubes of increasing dimension, each
corresponding to a dimension of the abstract simplicial complex. We show that
convergence in homomorphism density implies convergence in a cut-metric, and
vice versa, as well as showing that simplicial complexes sampled from the limit
objects closely resemble its structure. Applying this framework, we also
partially characterize the convergence of nonuniform hypergraphs.
