  We use a complete, unbiased sample of 257 dwarf (10^8 MSun < Mstar < 10^9.5
MSun) galaxies at z < 0.08, in the COSMOS field, to study the morphological mix
of the dwarf population in low-density environments. Visual inspection of
extremely deep optical images and their unsharp-masked counterparts reveals
three principal dwarf morphological classes. 43 and 45 per cent of dwarfs
exhibit the traditional `early-type' (elliptical/S0) and `late-type' (spiral)
morphologies respectively. However, 10 per cent populate a `featureless' class,
that lacks both the central light concentration seen in early-types and any
spiral structure - this class is missing in the massive-galaxy regime. 14, 27
and 19 per cent of early-type, late-type and featureless dwarfs respectively
show evidence for interactions, which drive around 20 per cent of the overall
star formation activity in the dwarf population. Compared to their massive
counterparts, dwarf early-types show a much lower incidence of interactions,
are significantly less concentrated and share similar rest-frame colours as
dwarf late-types. This suggests that the formation histories of dwarf and
massive early-types are different, with dwarf early-types being shaped less by
interactions and more by secular processes. The lack of large groups or
clusters in COSMOS at z < 0.08, and the fact that our dwarf morphological
classes show similar local density, suggests that featureless dwarfs in
low-density environments are created via internal baryonic feedback, rather
than by environmental processes. Finally, while interacting dwarfs can be
identified using the asymmetry parameter, it is challenging to cleanly separate
early and late-type dwarfs using traditional morphological parameters, such as
`CAS', M20 and the Gini coefficient (unlike in the massive-galaxy regime).
