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Community Bot
Community Bot
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It was asked herehere whether every functor is a composition of adjoint functors. The answer is no, because all adjoint functors induce homotopy equivalences on the nerve, and we can construct functors that do not induce homotopy equivalences.

My question is the following: can all functors inducing homotopy equivalences on the nerve be expressed as compositions of adjoint functors?

It was asked here whether every functor is a composition of adjoint functors. The answer is no, because all adjoint functors induce homotopy equivalences on the nerve, and we can construct functors that do not induce homotopy equivalences.

My question is the following: can all functors inducing homotopy equivalences on the nerve be expressed as compositions of adjoint functors?

It was asked here whether every functor is a composition of adjoint functors. The answer is no, because all adjoint functors induce homotopy equivalences on the nerve, and we can construct functors that do not induce homotopy equivalences.

My question is the following: can all functors inducing homotopy equivalences on the nerve be expressed as compositions of adjoint functors?

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David Corwin
David Corwin
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Is every functor inducing a homotopy equivalence a composition of adjoint functors?

It was asked here whether every functor is a composition of adjoint functors. The answer is no, because all adjoint functors induce homotopy equivalences on the nerve, and we can construct functors that do not induce homotopy equivalences.

My question is the following: can all functors inducing homotopy equivalences on the nerve be expressed as compositions of adjoint functors?