  In the previous part of this diptych, we defined the notion of an admissible
simplicial connection, as well as explaining how H.I. Green constructed a
resolution of coherent analytic sheaves by locally free sheaves on the \v{C}ech
nerve. This paper seeks to apply these abstract formalisms, by showing that
Green's barycentric simplicial connection is indeed admissible, and that this
condition is exactly what we need in order to be able to apply Chern-Weil
theory and construct characteristic classes. We show that, in the case of
(global) vector bundles, the simplicial construction agrees with what one might
construct manually: the explicit \v{C}ech representatives of the exponential
Atiyah classes of a vector bundle agree. Finally, we summarise how all the
preceding theory fits together to allow us to define Chern classes of coherent
analytic sheaves, as well as showing uniqueness in the compact case.
