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After studying the basics of (convex) optimization, I've become convinced there's sometimes a conceptual benefit in thinking of quantities like gradients etc. in a coordinate-free way, and keeping ...

The following useful lemma holds in a variety of settings: Lemma. Let $p : Y_1 \to X$, $p_2 : Y_2 \to X$ be fibrations over a common base, and $f : Y_1 \to Y_2$ a map over $X$ that is a homotopy ...

I would like to apologize for this rather stupid abstract nonsense question. Let $h=f\circ g$ for composable functors $f,g$; assume that there exist left or right adjoints to $f$ and $g$. Then it ...