Frobenius extensions play a central role in the link homology theories based
upon the sl(n) link variants, and each of these Frobenius extensions may be
recast geometrically via a category of marked cobordisms in the manner of
Bar-Natan. Here we explore a large family of such marked cobordism categories
that are relevant to generalized sl(n) link homology theories. We also
investigate the skein modules that result from embedding these marked
cobordisms within 3-manifolds, and arrive at an explicit presentation for
several of these generalized skein modules.Comment: 23 pages, multiple figure