The three great classical composers, Haydn, Mozart and Beethoven, are commonly referred to as the First Viennese School. They never really worked together as a group, though especially Mozart and Haydn knew each other well, and have most certainly influenced each other. For example, Mozart dedicated some string quartets to Haydn, because he valued Haydn’s string quartets so much.
The 6 string quartets (“the Haydn-Quartetts”) Mozart dedicated to Haydn (composed between 1782 – 1785), influenced by Haydn’s “russian quartets”:
string quartet G-Dur KV 387 (1782) – 1st Haydn-Quartet
string quartet d-moll KV 421 (1783) – 2nd Haydn-Quartet
string quartet Es-dur KV 428 (1783) – 3rd Haydn-Quartet
string quartet “Jagd-Quartett” (=”hunting quartet”) B-dur KV 458 (1783) – 4th Haydn-Quartet
string quartet A-dur KV 464 (1785) – 5th Haydn-Quartet
string quartet C- Dur “Dissonanzen-Quartett” KV 465 (1783) – 6th Haydn-Quartet
In general they valued each other very much as composers, and as persons. For Beethoven, who was the “youngest” of the three, the other two were his big examples.