If I am writing a poem, I might use the word peaches to symbolize all fruit. Is there a specific word for this type of symbolism?
It's called metonymy. For example, sword for "war" or Washington for "the US Government".
If you're interested in a suitable word outside the realm of literary criticism, you might consider exemplar especially if you're looking for the connotation of the single best representation of the many.
Wiktionary gives the definition of:
Something typical or representative of a class
Something fit to be imitated
I'd use "syndedoche" in the sense of the original question- use of a subset of something to represent the whole, e.g. "The colonel commanded two hundred horse", or "Fifty head of cattle"
As I understand it, metonymy is the use of something associated with the described object as a representation of it; "Hollywood" for the film industry, or "Wall Street" for the financial market.