Speed relationship to the operational amplifier speed

Dear friends,

it is know that shorter channel transistor is faster than with longer gate. This I can understand well when we talk about NOSFET working as a switch.

But how this concept affect the speed of the operational amplifier where GBW = gm / CL for example. If you tell me that shorter channel leads to higher gm I can say that gm can be increased by increasing W or the biasing current, secondly the formula shows that only the input differential transistors affect the GBW, other transistors in the op-amp are not exsisting in the GBW last equation.

Thank you in advance

Equations only tell you, what their author told them.
Equations are always (or at best) simplifications of
reality.

When most people talk about "shorter gate" being
"faster" they often talk at "high level" comparing a
(say) 90nm transistor to a 250nm transistor. The
channel gm is higher, true. But "speed" has other
elements such as the drawn drain area (Cdb) and
spacer geometry / contact-to-poly spacing (Cdg,
the big deal for FET fT/fmax along with Rg, and you
cannot leave Rg out as it's another highly groundrule
and process-details dependent factor.

In an uncompensated OTA, maybe the other transistors
are not small-signal-significant. However they may have
influence on large signal transient attributes; front end
current steering per delta-V (diff pair gm) is limited at
very small signal and limits bandwidth at "nil plus a nit"
overdrive.