# ag.algebraic geometry – Freyd non-concreteness in motivic homotopy theory

The following theorem is due to Freyd.

Let $$C$$ be a category of pointed topological spaces including all finite-dimensional CW-complexes. Let $$H:Cto mathrm{Set}$$ be a homotopy invariant functor. There exists $$f:Xto Y$$ such that $$f$$ is not null-homotopic but $$H(f)=H(star)$$ where $$star$$ is null-homotopic.

Is there an analogue of this theorem in motivic homotopy theory?