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\xymatrix @=9pt { |
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A(X') \ar[rr] \ar[dd] \ar[dr] && A(\Delta[n]) \arfib'[d][dd] \arwe[dr] & \\ |
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& C^\ast(X') \ar[rr] \ar[dd] && C^\ast(\Delta[n]) \arfib[dd] \\ |
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A(X) \ar'[r][rr] \arwe[dr] && A(\del\Delta[n]) \arwe[dr] & \\ |
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& C^\ast(X) \ar[rr] && C^\ast(\del\Delta[n]) |
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} |
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\xymatrix{ |
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\del\Delta[n] \ar[r] \ar[d] \xypo & X \ar[d] \\ |
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\Delta[n] \ar[r] & X' |
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} |
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\xymatrix{ |
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\DELTA \ar[d]^{\Delta[-]} \ar@<+.6ex>[drr]^-\Apl && \\ |
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\sSet \ar@{-->}@<+.6ex>[rr]^-A & \xyadj & \CDGA_\k^{op} \ar@{-->}@<+.6ex>[ll]^-K |
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} |
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\xymatrix{ |
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\DELTA \ar[d]^{\Delta[-]} \ar@<+.6ex>[drr]^-C && \\ |
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\sSet \ar@{-->}@<+.6ex>[rr]^-{C^\ast} & \xyadj & \DGA_\k^{op} \ar@{-->}@<+.6ex>[ll] |
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} |
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\xymatrix{ |
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\DELTA \ar[d]^{\Delta[-]} \ar@<+.6ex>[drr]^-F && \\ |
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\sSet \ar@{-->}@<+.6ex>[rr]^-{F_!} & \xyadj & \cat{C} \ar@{-->}@<+.6ex>[ll]^-{F^\ast} |
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} |
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\xymatrix{ |
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\cdots \ar[r] & H_{i+1}(E^{k+1}, E^k) \ar[r] \ar[d] & H_i(E^k, F) \ar[r] \ar[d] & H_i(E^{k+1}, F) \ar[r] \ar[d] & \cdots \\ |
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\cdots \ar[r] & H_{i+1}(B^{k+1}, B^k) \ar[r] & H_i(B^k, b_0) \ar[r] & H_i(B^{k+1}, b_0) \ar[r] & \cdots |
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} |
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\xymatrix{ |
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\pi_n(X(n)) \ar[r]^\iso \ar[d]^\iso & H_n(X(n)) \ar[d]^{\C-iso} \\ |
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\pi_n(X) \ar[r] & H_n(X) |
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} |
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\xymatrix{ |
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\cdots \ar[r] & \pi_{i+1}(B_f, A) \ar[r] \ar[d] & \pi_i(A) \ar[r]^{f_\ast} \ar[d] & \pi_i(B) \ar[r] \ar[d] & \pi_i(B_f, A) \ar[r] \ar[d] & \cdots \\ |
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\cdots \ar[r] & H_{i+1}(B_f, A) \ar[r] & H_i(A) \ar[r]^{f_\ast} & H_i(B) \ar[r] & H_i(B_f, A) \ar[r] & \cdots \\ |
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} |
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