motivic function



Given a small category 𝒞\mathcal{C} with coproducts and given an object X𝒞X \in \mathcal{C}, the abelian group Mot(X)Mot(X) of motivic functions on XX is defined by generators and relations as follows: it is the quotient of the free abelian group on the morphisms SXS \to X by the relations

[S 1S 2(f 1,f 2)X]=[S 1f 1X]+[S 1f 2X]. [S_1 \coprod S_2 \stackrel{(f_1,f_2)}{\to} X] = [S_1 \stackrel{f_1}{\to} X] + [S_1 \stackrel{f_2}{\to} X] \,.

The construction of motivic functions has some similarity with


Section 2.2 of

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