Crates didn't create the first globe of the earth. This myth comes from a mistranslation of a passage in Strabo, Geography 2.5.10 (the mistranslation is present in the edition I've linked). This passage is the only source that can be (mis)construed as hinting at Crates' 'globe'.

Crates was no cartographer or engineer. He was a very bookish literary critic who wrote commentaries on Greek poetry. None of his works survive except in second-hand references: the standard edition of the fragments is Maria Broggiato's Cratete di Mallo: I frammenti (2001).

We know that in Crates' commentary on the Odyssey he happened to talk about the spherical geometry of the earth: he took the rather cringeworthy stance that Homer was a genius who already knew all about the zones of the earth, ranging from the polar region to the equator, as described by figures like Eratosthenes (Crates F 54 Broggiato; for Eratosthenes' zones see Eratosthenes, Geography F 30, F 45 ed. Roller); and that Homer's Aithiopes live in both the summer tropic and the winter tropic, that is, the bands of latitude corresponding to the Tropics of Capricorn and Cancer, with an uninhabitable zone in between the two tropics (Crates F 37 Broggiato).

So the key passage in Strabo, in its mistranslated form, goes

... the man who would most closely approximate the truth by constructed figures must needs make for the earth a globe like that of Crates, and lay off on it the quadrilateral, and within the quadrilateral put down the map of the inhabited world. But since there is need of a large globe ... it is better for him to construct a globe of adequate size, if can do so; and let it be no less than ten feet in diameter.

So this produces a double-whammy of myths: (1) Crates made a globe, (2) Crates' globe was ten feet across.

We can already dismiss the ten-foot-wide part of the myth, because that isn't what Strabo says even in this translation. He just says that if someone wants to represent the geometry of the known world properly, then their globe would need to be ten feet across.

As for the first bit: the key phrase in Strabo (= Crates F 134 ed. Broggiato) --

ποιήσαντα σφαῖραν τὴν γὴν, καθάπερ τὴν Κρατήτειον

must make for the earth a globe like that of Crates (tr. Sterrett and Jones)

really means

must treat the earth as a sphere, like the Cratetean (system)

-- that is, he's referring to the system of zones that Crates is referring to when he talks about the Aithiopes and the Kimmerioi. This has not prevented a number of scholars, including Broggiato herself, from repeating the myth.