  In this work we discuss the construction of "simplicial BF theory", the field
theory with finite-dimensional space of fields, associated to a triangulated
manifold, that is in a sense equivalent to topological BF theory on the
manifold (with infinite-dimensional space of fields). This is done in framework
of simplicial program - program of constructing discrete topological field
theories. We also discuss the relation of these constructions to homotopy
algebra.
