Inverse limit

Corollary. Every affine group scheme G over a field is an inverse limit of algebraic affine group schemes. 

The set of all such v7 is principal homogeneous under the group Horn (G, M). But this group is zero because it can be written as lim Horn (G(n), M). If (

[Pg.147]

Consider now the inverse limiting case inorganic quantum wells. In this case the excitons in layer 1 are two-dimensional and... 

Exercise 2.3.9. Show that if is a Grothendieck category then D(X) is equivalent to the homotopy category of q-injective complexes. Hence if A has inverse limits then so does D(yl). 

Proof. — The first statement is obvious. The second follows from the fact that an inverse limit of a tower of weak equivalences of simplicial sets is a weak equivalence at least if all the morphisms in the towers are fibrations. 

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