Context :

Aims : We analyse the properties of the early-type dwarf galaxy population ( M _ { V } > -17 mag ) in the Hydra I cluster .
We investigate the galaxy luminosity function ( LF ) , the colour–magnitude relation ( CMR ) , and the magnitude–surface brightness relation down to M _ { V } \sim - 10 mag .
Another goal of this study is to find candidates for ultra-compact dwarf galaxies ( UCDs ) in Hydra I .

Methods : Two spectroscopic surveys performed with Magellan I/LDSS2 at Las Campanas Observatory and VLT/VIMOS , as well as deep VLT/FORS1 images in V and I bands , covering the central parts of the cluster , were examined .
We identify cluster members by radial velocity measurements and select other cluster galaxy candidates by their morphology and low surface brightness .
The candidates ’ total magnitudes and central surface brightnesses were derived from the analysis of their surface brightness profiles .
To determine the faint-end slope of the LF , the galaxy number counts are completeness corrected .

Results : We obtain radial velocities for 126 objects and identify 32 cluster members , of which 5 are previously uncatalogued dwarf galaxies .
One possible UCD candidate with M _ { V } = -13.26 mag is found .
Our sample of \simeq 100 morphologically selected dwarf galaxies with M _ { V } > -17 mag defines a CMR that extends the CMR of the giant cluster galaxies to the magnitude limit of our survey ( M _ { V } \sim - 10 mag ) .
It matches the relations found for the Local Group ( LG ) and the Fornax cluster dwarf galaxies almost perfectly .
The Hydra I dwarf galaxies also follow a magnitude–surface brightness relation that is very similar to that of the LG dwarf galaxies .
Moreover , we observe a continuous relation for dwarf galaxies and giant early-type galaxies when plotting the central surface brightness \mu _ { 0 } of a Sérsic model vs. the galaxy magnitude .
The effective radius is found to be largely independent of the luminosity for M _ { V } > -18 mag .
It is consistent with a constant value of R _ { \mathrm { e } } \sim 0.8 kpc .
We present the photometric parameters of the galaxies as the Hydra I Cluster Catalogue ( HCC ) .
By fitting a Schechter function to the luminosity distribution , we derive a very flat faint-end slope of the LF ( \alpha = -1.13 \pm 0.04 ) , whereas fitting a power law for M _ { V } > -14 mag gives \alpha = -1.40 \pm 0.18 .

Conclusions : Our findings of a continuous CMR and \mu _ { 0 } – M _ { V } relation for dwarf and giant early-type galaxies suggests that they are the same class of objects .
The similarity of those relations to other environments like the LG implies that internal processes could be more important for their global photometric properties than external influences .