Sheaf model

Uniqueness I claim that any complete non-singular model, regarded as a topological space plus a sheaf of rings, is nothing but the following ... 

It is easy to see that our claim will follow if we show that the sheaves pointed maps from any model of the i-sphere to 3 ). 

L roof — Let be a resolution functor on the category of cosimplicial simplicial sets (with respect to the standard closed model structure described in [3]). Below we use the equality sign instead of specifying explicit weak equivalences. Unless otherwise specified functors on cosimplicial simplicial sets are extended to functors on cosimplicial simplicial presheaves pointwise. The functor of associated sheaf is denoted by a. We have... 

Choose a resolution functor (Ex, 0) (see 1.6) corresponding to the simplicial model category structure on A Shv(T). Thus for any simplicial sheaf 36 the morphism —> Ex. ) is a (simplicial) weak equivalence and Ex(36 ) is (simplicially) fibrant. 

Electron microscopy on thin films [2-5] led to Peterlin s sphemlite model [6] consisting of a sheaf-shaped nucleus growing under radial-symmetric formation of lamellar stmctures. Within the lamellae Kanig [7] found inclination of chain-segments using a special contrasting procedure. 

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