By Klein F.
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Extra resources for Vorlesungen ueber die hypergeometrische Funktion
1) and let T : C—>D be a functor of sections. Let p 0 denote the pasting functor. (A) If $ 0 and $t are functors of sections Cp—>D such that $ 0 ° p 0 and ^j^Po are functorially equivalent, then $ 0 and $ t are functorally equivalent. (B) Suppose for each canopy G over C, the graph T(G) admits a colimit in D. Then there exists a functor of sections $ : CD—>D such that $op 0 = r. Proof: p a r t (A) is trivial. (B) Assume that the image each canopy of C under T admits a colimit. For each G e CD, let PIG] :r(G)—>$0(G) be a colimit; for Ce C, choose $(CD) = r(C) and (MCP]= l r ( c ) .
B) the class T, of all subsets S c Cov which are subsets of J, is a set. Cov satisfies the smallness condition if each A c C admits a choice of representatives with topology. A class-theoretic function which assigns to each A e C a choice of representatives w i t h topology over A is called a categorical choice of representatives w i t h topology for C. For the rest of this section, assume (C,Sub,Cov) is a topologized category. The universe of subsets associated to C and its topology are denoted respectively by Sub (or Sub*») and Cov (or Cov*»).
Composing two layered Paul Feit 32 morphism s yields a m e m b e r of Lay, so t h e first projection X X ^X—>X is a L a y morphism . Hence, Sub t is a universe of subsets. Obviously Covx is a topology over Sub x . (C) and (D) are immediate. (B) Suppose b^B—>A is a covering m o r p h i sm w i t h respect to Covj. Projection B X ^B—>B c a n be regarded as a pullback of b along a covering morphism. 12) implies b e Lay. (E) Assume both Lay and Sub are universes of embeddings. Let b : Y—>Z and c : X—>Y be C-morphisms suc h t h a t b , b o c e Sub t .
Vorlesungen ueber die hypergeometrische Funktion by Klein F.