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# Questions

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### Why forgetful functors usually have LEFT adjoint?

jan 1 10 at 19:04 Reid Barton 14.4k12885

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### Why is the decomposition theorem awesome?

dec 9 09 at 4:52 Ben Webster 20.7k144114

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### Which algebraic varieties admit a morphism to a curve?

aug 15 10 at 7:28 ABayer 1,4741917

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### Why are finiteness conditions important (and how to recognize them)?

apr 3 12 at 17:42 Ostap Chervak 2221410

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### Is there a “knot theory” for graphs?

oct 31 11 at 21:08 Roberto Frigerio 1,849514

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### What’s the easiest example of a morphism of topoi that is not from that of a site?

apr 17 12 at 15:43 Filippo Alberto Edoardo 1,682512

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### Why does the (S2) property of a ring correspond to the Hartogs phenomenon?

oct 13 at 1:41 Sándor Kovács 23.8k25273

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### How does one motivates the method of separation of variables when teaching PDE’s?

nov 16 10 at 13:54 Bob Terrell 42816

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### Does the derived category remember the homological dimension?

mar 5 11 at 19:18 Mariano Suárez-Alvarez 30.6k768153

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