Given a small category $\mathcal{C}$ with coproducts and given an object $X \in \mathcal{C}$, the abelian group $Mot(X)$ of motivic functions on $X$ is defined by generators and relations as follows: it is the quotient of the free abelian group on the morphisms $S \to X$ by the relations
The construction of motivic functions has some similarity with
the construction of Baum-Douglas geometric cycles
the construction that Baez-Dolan called de-groupoidification.
Section 2.2 of
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