  The Fornax Deep Survey (FDS), an imaging survey in the u', g', r', and
i'-bands, has a supreme resolution and image depth compared to the previous
spatially complete Fornax Cluster Catalog (FCC). Our new data allows us to
study the galaxies down to r'-band magnitude m$_{r'}\approx$21 mag
(M$_{r'}\approx$-10.5 mag). These data provide an important legacy dataset to
study the Fornax cluster. We aim to present the Fornax Deep Survey (FDS) dwarf
galaxy catalog, focusing on explaining the data reduction and calibrations,
assessing the quality of the data, and describing the methods used for defining
the cluster memberships for the catalog objects. As a first step we used the
SExtractor fine-tuned for dwarf galaxy detection, to find galaxies from the FDS
data, covering a 26 deg$^2$ area of the main cluster, and the area around the
Fornax A substructure. We made 2D-decompositions of the identified galaxies
using GALFIT. We used color-magnitude, luminosity-radius and
luminosity-concentration relations to separate the cluster galaxies from the
background galaxies. We then divided the cluster galaxies into early- and
late-type galaxies according to their morphology and gave first order
morphological classifications. Our final catalog includes 14,095 galaxies. We
classify 590 galaxies as being likely Fornax cluster galaxies, of which 564 are
dwarfs (M$_{r'}$ > -18.5 mag) consisting our Fornax dwarf catalog. Of the
cluster dwarfs we classify 470 as early-types, and 94 as late-type galaxies.
Our final catalog reaches its 50% completeness limit at magnitude M$_{r'}$ =
-10.5 mag and surface brightness $\bar{\mu}_{e,r'}$ = 26 mag arcsec-2, which is
approximately three magnitudes deeper than the FCC. Based on previous works and
comparison with a spectroscopically confirmed subsample, we estimate that our
final Fornax dwarf galaxy catalog has < 10% contamination from the background
objects.
