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The naive approach to deriving profunctors - What's wrong with it?
Let $(\mathcal{C,W})$ be relative category (equipped with a wide subcategory of weak equivalences satisfying 2 out of 3 property). Consider a profunctor $F: \mathcal{C \times D^{op}} \to \mathsf{Set}$ …
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What is integration along the fibers in D-module theory?
(All functors and categories are derived, all $\mathcal{D}$-modules are holonomic and $f: X \to Y$ is proper for simplicity).
We may use the adjunction $\int_f \dashv f^!$ to get some interpretation …