The caudate lobe of liver corresponds to which segment of Counaud's classification :
Caudate lobe is segment I
Quadrate lobe is segment IVa
The caudate lobe (segment I) is the dorsal portion of the liver and embraces the IVC. It lies posterior to the left portal triad inferiorly and left and middle hepatic vein superiorly.

Caudate lobe is unique in sense that

it receives blood supply from both the right & left portal pedicles.
bile ducts drain into both right & left hepatic ducts.
its venous drainage is directly into the vena cava
Segment I
Segment II
Segment III
Segment IV