Timeline for Is every functor inducing a homotopy equivalence a composition of adjoint functors?
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| Dec 28, 2012 at 13:45 | comment | added | Eric Wofsey | A totally different way to get a counterexample: note that any composition of adjoints must have a functor going the other way which provides a homotopy inverse on nerves (namely, the composition of all the adjoint functors going the other way). It's easy to construct examples of finite posets $X$ and $Y$ such that there is a map $X\to Y$ inducing an equivalence but no map $Y\to X$ inducing an equivalence. | |
| Dec 28, 2012 at 13:01 | history | answered | Eric Wofsey | CC BY-SA 3.0 |