The $K’$–theory of monoid sets

Algebraic $$K\!$$-theory and Grothendieck–Witt theory of monoid schemes

“…In [3,Theorem 5.17] it is shown that the missing relations can be recovered by a comparison morphism between K-theory and G-theory. In [17,Theorem 5.7] it is shown that the Ktheory of P n F 1 is as expected, where K -theory is defined in terms of sheaves that locally come from finitely generated partially cancellative modules. Neither of these approaches extend to Grothendieck-Witt theory and hence we do not pursue them further in the present paper.…”

“…Following earlier approaches [10,19], a general definition of the K-theory of a monoid scheme X was given in [3], where a proto-exact category of vector bundles Vect(X ) and their normal O X -module homomorphisms was defined. We point out that this is not the only approach to the K-theory of monoid schemes; see [17] for a recent alternative. In Sect.…”

“…The K-theory of pointed monoids has been studied by a number of authors [3,4,10,17]. In this section we describe those results which are relevant to this paper.…”