I've seen a few posts say what the "regs" say, but no-one has actually posted or quoted the actual regulation that
defines the categories.
Can I suggest Part 97,
Section 97.3:
Sec. 97.3
Symbols and terms used in procedures.
[As used in the standard instrument procedures prescribed in this part--
Aircraft approach category means a grouping of aircraft based on a speed of VREF, if specified, or if VREF is not specified, 1.3 Vso at the maximum certificated landing weight. VREF, Vso, and the maximum certificated landing weight are those values as established for the aircraft by the certification authority of the country of registry. The categories are as follows--
(1) Category A: Speed less than 91 knots.
(2) Category B: Speed 91 knots or more but less than 121 knots.
(3) Category C: Speed 121 knots or more but less than 141 knots.
(4) Category D: Speed 141 knots or more but less than 166 knots.
(5) Category E: Speed 166 knots or more.
Note that the 1.3 times stall speed only applies if VREF is not defined - since I'm pretty sure the 737 has an explicitly defined VREF, that's what counts, not some arbitrary factor of stall speed. (Which makes sense, after all, it's what you're being told to fly).