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Per this page, Deere has over 30% of the market; I don't know that would be considered a monopoly, but assuming the rest of the market is heavily fragmented, it's certainly a dominant position.

https://csimarket.com/stocks/compet_glance.php?code=DE

I think Deere has about 25-35% of the market, with New Holland and Kubota in there afterwards

True. My usual very-unscientific method is a search for "john deere vs" which turned up some alternatives but they seemed to be obscure to the point of giving Deere an effective monopoly, but yeah I don't really know.

Driving through rural Texas I've even seen a Tata dealership.