It's a B double flat, or Bbb, not an A. This is an enharmonic spelling to stay consistent with the chordal notes because C chords don't contain an A.
Dim 7s are 3 minor third intervals stacked on one another.
So you have a diminished triad, and a diminished 7th.
C Eb Gb Bb, is a diminished triad with a minor seventh. This is called a half diminished chord or minor 7 flat 5 depending if you're in classical or jazz circles.