Towards a Categorical Model of the Lilac Separation Logic
summary
Constructs two categories—a probabilistic “sheaf/topos–style” category and a nominal-style category—and proves they are equivalent, so Lilac’s independent combination corresponds to ordinary product spaces under that equivalence. Uses category‑theoretic tools (Day convolution, sheaf constructions) together with measure‑theoretic constructions of probability spaces to show the separating conjunctions match, isolating which measure‑theoretic side conditions are essential and which are artifacts of the original model.
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