WebbIn the category of abelian groups and group homomorphisms, Ab, an injective object is necessarily a divisible group. Assuming the axiom of choice, the notions are equivalent. In the category of (left) modules and module homomorphisms, R - Mod, an injective object is an injective module. Webb26 okt. 2024 · AC-Gorenstein rings and their stable module categories James Gillespie We introduce what is meant by an AC-Gorenstein ring. It is a generalized notion of Gorenstein ring which is compatible with the Gorenstein AC-injective and Gorenstein AC-projective modules of Bravo-Gillespie-Hovey.
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Webbde ne the homotopy category Ho(C) of a model category Cto be the category whose objects are the bi brant (i.e. co brant and brant) objects of Cand whose morphisms are … Webb13 juni 2024 · Given a symmetric monoidal model category C, Schwede and Shipley have given conditions under which the category of monoids in C is again a model category (with underlying fibrations and weak equivalences). On the other hand, the category of commutative monoids seems to be much more subtle. misty buscher donald trump
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WebbQuillen model categories. In order to do so, we establish the existence of projective and injective model structures on diagram 2-categories. Using these results, we describe … WebbRecently, Hovey has shown that model category structures naturally arise from small cotorsion pairs over C(Qco(X)), [20]. Since Qco(X) is a Grothendieck cat-egory [8], there is a canonical injective model category structure on C(Qco(X)). However, this structure is not monoidal, that is, compatible with the tensor product on Qco(X), [21, pp. 111-2]. Webb22 jan. 2013 · The category of quasi-coherent sheaves is Grothendieck and the class Flat (X) of flat quasicoherent sheaves is deconstructible. So by [Sto13, Theorem 3.16] we get that Flat (X) inherits the... misty burton