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Created product-preserving functor.
Added a link to preserved limit.
I added some remarks about flat functors.
I definitely write “product-preserving functor”, but can someone help me decide whether I should write “finite-product-preserving functor”, “finite product preserving functor”, or something else? I can never make up my mind. I lean towards f-p-p, but there’s such a thing as too many hyphens in a row.
You could try ‘finite-product–preserving functor’. (That’s one hyphen and one en dash.) Or else cartesian monoidal functor (following cartesian monoidal category), which already exists but could use explication and redirects.
I’ve written “finite-product-preserving” and “finite-product preserving”, with the same misgivings as Tom. Other than that, circumlocutions like “functor preserving finite products”. Maybe “cartesian” or “cartesian monoidal” on odd occasions.
I’ve only just now thought of “fpp functor” as perhaps acceptable in a paper where the phrase is invoked often, with an explanatory note at the beginning.
Just make sure it is not confused with fppf.
Thanks for the opinions. Toby’s solution is kind of hilarious, and makes me want to coin some phrase such as “Birch–Swinnerton-Dyer–proving construction”. I hadn’t thought of cartesian monoidal: not bad, but not one to use just in passing.
Wikipedia cops out with ‘Birch and Swinnerton-Dyer conjecture’. No fun, Wikipedia! (Especially since the masters of the WP Manual of Style know how to use en dashes perfectly well.)
Edit: missing word ‘since’.
+1 Tom ;-)
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