Gerry Mulligan Quartet
Founded by Baritone Saxophonist Gerry Mulligan, later Miles Davis would join this to try to incorporate the idea of cool jazz.
A lot of these people were from the West Coast (see the image). They even mentioned how people like Charlie Parker could only survive in NYC and on the east coast. The west coast Bebop (Bop) never took off, but cool jazz did take off.