Neurology Mathematics Ideas120.pdf - i Let us describe the functor Gn,κ in detail First note that for z1ǫ1 ⊠ � � � ⊠ znǫn ∈ T(Sn,κ and ǫi =

Neurology Mathematics Ideas120.pdf - i Let us describe the...

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Let us describe the functor G ( i ) n,κ in detail. First note that for z ǫ 1 1 · · · z ǫ n n T( S n,κ ) and ǫ i = 1 the object Hom A ( z i , 1 ) z ǫ 1 1 · · · hatwider z ǫ i i · · · z ǫ n n T( S ( i ) n,κ ) (C.7) (with the symbol hatwide z indicating that the factor z is to be removed from the expression) comes canonically with the following balancings: For a ∈ A the balancing between z i 1 and z i +1 is, in case the orientations are as in the picture (C.3), Hom A ( z i , 1 ) z i 1 .a z i +1 = Hom A ( z i , 1 ) ( z i 1 a ) z i +1 = Hom A ( z i [ κ i ] a, 1 ) z i 1 z i +1 = Hom A ( z i , [ κ i 1] a ) z i 1 z i +1 = Hom A ( [ κ i 2] a z i , 1 ) z i 1 z i +1 = Hom A ( z i , 1 ) z i 1 z i +1 . [ κ i + κ i +1 ] a, (C.8) and similarly for other combinations of orientations. In these expressions we display only the relevant part of the object, and we use the balancings of the object z ǫ 1 1 · · · z ǫ n n in steps two
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