Let V be a ℂ-space, $\sigma \in End\left(V^{\otimes 2}\right)$ be a pre-braid operator and let $F\in lin(V^{\otimes 2},ℂ).$ This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra $Cl(V,\sigma ,0)\equiv V^{\wedge }\left(\sigma \right)$. If $\sigma \ne {\sigma }^{-1}$ and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...