set one's cap at

English edit

Probably a calque of French mettre le cap sur (“to set a course for”).

set one's cap at (third-person singular simple present sets one's cap at, present participle setting one's cap at, simple past and past participle set one's cap at)

(idiomatic) To choose a man as a potential husband (for a girl).
- 1863, Sheridan Le Fanu, The House by the Churchyard:
  To hear her rant, one would have supposed, who had not seen him, that her lank-haired, grimly partner, was the prettiest youth in the county of Dublin, and that all the comely lasses in Chapelizod and the country round were sighing and setting caps at him […]
(idiomatic, more generally) To choose something as a goal.
- Patrick O'Brian, "HMS Surprise".
  How he has escaped marriage until now I cannot tell: the number of caps set in his direction would furnish a warehouse.

to choose a man as a potential husband for a girl

to choose something as a goal