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678 |
679 %We will aim for a little bit more generality than we need and not assume that the objects |
679 %We will aim for a little bit more generality than we need and not assume that the objects |
680 %of our auxiliary category are sets with extra structure. |
680 %of our auxiliary category are sets with extra structure. |
681 First we must specify requirements for the auxiliary category. |
681 First we must specify requirements for the auxiliary category. |
682 It should have a {\it distributive monoidal structure} in the sense of |
682 It should have a {\it distributive monoidal structure} in the sense of |
683 \nn{Stolz and Teichner, Traces in monoidal categories, 1010.4527}. |
683 \cite{1010.4527}. |
684 This means that there is a monoidal structure $\otimes$ and also coproduct $\oplus$, |
684 This means that there is a monoidal structure $\otimes$ and also coproduct $\oplus$, |
685 and these two structures interact in the appropriate way. |
685 and these two structures interact in the appropriate way. |
686 Examples include |
686 Examples include |
687 \begin{itemize} |
687 \begin{itemize} |
688 \item vector spaces (or $R$-modules or chain complexes) with tensor product and direct sum; and |
688 \item vector spaces (or $R$-modules or chain complexes) with tensor product and direct sum; and |