Your supplier is correct.
ASTM A36 is viewed generally as a plate steel, with reference for general specifications requirements to ASTM A6.  A6 states hot-rolled plate is generally defined as material 0.230" (6 mm) or thicker for widths 8" - 48" and material 0.180" (4 mm) or thicker for over 48 " in width.
ASTM A1011 is defined as a sheet steel.  For hot-rolled sheet, the general specification ASTM A568 indicates an upper limit of 0.230" (6 mm) for basically all widths.  The range 4mm to 6mm is a bit of a gray area at the moment.
ASTM A1011 Grade 36 Type 2 was intended to match ASTM A36 plate steel as close as possible in a sheet thickness.

I concur, the supplier is correct with providing ASTM A 1011 SS (structural steel) Grade 36.

Thanks ajh1,

I understand your explanation, but... do you know some technical paper or literature where it is confirmed?, i.e. some ASTM standard?
About the correct equivalence: ASTM A36 vs ASTM A1011,... is Grade 36 Type 1 or Type 2?.
Regards.

Not sure what you mean by confirmed.  The information I gave is straight from the various ASTM standards themselves.  I'm on the ASTM committees that handle both of these standards, and my recollection was that A1011 Grade 36 Type 2 was added specifically for the A36 compatibility.  The clue is that the tensile limits are set to match A36.