  We present a study of nearby galaxies as a function of their [3.4]-[4.6]
colour. Galaxies that are red in their [3.4]-[4.6] colour contain heated dust
and the reddest systems ([3.4]-[4.6] > 0.5) are classified as AGN by some
selection criteria. The sample discussed here includes nearby galaxies selected
from the Sloan Digital Sky Survey (SDSS) that are also in the Wide-field
Infrared Survey Explorer (WISE) catalogue. We calculate the number density of
galaxies, in the form of the luminosity and mass functions, using the V/Vmax
method and a Stepwise Maximum Likelihood method that has been modified to
account for the additional colour selection. The reddest galaxies which have
[3.4]-[4.6] > 0.8 and are sometimes classified as AGN by their colour, make up
0.2% of nearby galaxies. However, the reddest galaxies are a rising fraction of
the low mass galaxy population. Identifying the lowest mass (M < 10$^{8}$
M$_{\odot}$ ) red ([3.4]-[4.6] > 0.8) galaxies as AGN is surprising given that
none are optical AGN or composites, in contrast with their more massive (M >
10$^{10}$ M$_{\odot}$ ) red galaxy counter- parts that are dominated by optical
AGN and composites (86.4%). We also show that these low mass red galaxies are
associated with higher specific star formation rates than their bluer
counterparts. While the properties of this relatively rare segment of nearby
low-mass galaxies are intriguing, particularly if they are associated with AGN
activity, there is not yet enough evidence to determine whether it is AGN or
unusual star formation that is driving red colours in these systems.
