  We introduce tropical complexes, as an enrichment of the dual complex of a
degeneration with additional data from non-transverse intersection numbers. We
define cycles, divisors, and linear equivalence on tropical complexes,
analogous both to the corresponding theories on algebraic varieties and to
previous work on graphs and abstract tropical curves. In addition, we establish
conditions for the divisor-curve intersection numbers on a tropical complex to
agree with the generic fiber of a degeneration.
