aggregate in category theory?

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Jun 18, 2023 at 19:17	comment	added	Tom Copeland		In this last comment on "a field of coins of lines of piles of coins" every noun refers to countable structures, not a single substance hence 'a field' = 'one unspecified field' and 'lines', 'piles', and 'coins' are in their plural forms. If the application of the category theory of the paper is correctly interpreted by the user, this is a singular failure of the theory in understanding (the English) language. I've never heard the phrase 'a field of water' rather than say 'a body of water'.
May 3, 2021 at 23:37	comment	added	user164898		I only skimmed the paper, but it seems that they regard count nouns as sets, and mass nouns as sup-lattices. You have an free-forgetful adjunction between sets and sup-lattices, and phrases that involve both mass and count nouns (e.g. "this steak is meat") are interpreted by means of that adjunction. In the paper's proposed semantics, I imagine that a phrase like "a field of lines of piles of coins," involving multiple transitions between mass and count nouns, would simply require using that adjunction several times. (This begins to seem a bit like the bar construction.)
May 3, 2021 at 17:40	comment	added	Tom Copeland		I have trouble fitting a pile of sand, a pile of coins, a line of sand, a line of coins, a field of ... , or a drop of water suspended in the air in the space station into the scheme of Reyes et al. Perhaps you can enlighten me.
May 3, 2021 at 6:30	history	answered	Tim Campion	CC BY-SA 4.0