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The Cahiers topos is the sheaf topos on the siteThCartSp of infinitessimally thickened cartesian spaces. More generally the higher cahiers topos is the $(\infty,1)$-sheaf $(\infty,1)$-topos on the $(\infty,1)$-site ThCartSp.

However the $(\infty,1)$-topos arising in this way is (still) a 1-localic (i.e. localic) $(\infty,1)$-topos; in other words this notion of higher cahiers topos is no more intelligible than just the classical cahiers topos.