Were The Grateful Dead a jazz band?

[LuckyCharms]

Phil Lesh (Grateful Dead bass guitarist) talks about the influences of Miles Davis and John Coltrane:

"The basic inspiration for The Grateful Dead was the Miles Davis Quartet with Coltrane or Trane's quartet from the early Sixties. So that was pretty much the inspiration for the way we approach our music."

Miles Davis on Jerry Garcia:

So it was through Bill Graham that I met the Grateful Dead. Jerry Garcia, their guitar player, and I hit it off great, talking about music - what they liked and what I liked - and I think we all learned something, grew some. Jerry Garcia loved jazz, and I found out that he loved my music and had been listening to it for a long time. He loved other jazz musicians, too, like Ornette Coleman and Bill Evans.”
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LuckyCharms: I've always heard The Grateful dead as predominantly a jazz band, with rock, R&B, folk, classical, Motown and bluegrass influences.

Below is some audio I found which displays pretty much all of these styles rolled into one band, and I don't believe there will be another musical collaboration like the Grateful Dead ever again.

This is a compilation of the Grateful Dead playing various iterations of "Feeling Groovy" and "Tighten Up" from the late 60s and early 70s. Some amazing and musically complicated interpretations in here...something nice to put on and give a good listen to as you try to discern each individual instrument. I hear a lot of Miles Davis and John Coltrane influenced themes in here...not directly, but stylistically.