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Five faces of an algebraic category

November 23, 2012

Face 1.

({odd, even}, +)

({neg., pos.}, x)

Face 2.

f: A -> B

A = {odd, even}, B = {neg., pos.}

f (ai + aj) = f (ai) x f (aj)

f (odd + odd) = f (odd) x f (odd)

f (odd + even) = f (odd) x f (even)

f (even + odd) = f (even) x f (odd)

f (even + even) = f (even) x f (even)

Face 3.

odd + odd = even

odd + even = odd

even + odd = odd

even + even = even

f (even) = f (odd) x f (odd)

f (odd) = f (odd) x f (even)

f (odd) = f (even) x f (odd)

f (even) = f (even) x f (even)

Face 4.

f (odd) = neg.

f (even) = pos.

Face 5.

pos. = neg. x neg.

neg. = neg. x pos.

neg. = pos. x neg.

pos. = pos. x pos.

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