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A note on model structures on arbitrary Frobenius categories

Zhi-wei Li (2017)

Czechoslovak Mathematical Journal

We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category ℱ such that the homotopy category of this model structure is equivalent to the stable category ℱ ̲ as triangulated categories. This seems to be well-accepted by experts but we were unable to find a complete proof for it in the literature. When ℱ is a weakly idempotent complete (i.e., every split monomorphism is an inflation) Frobenius category, the model structure we constructed is an exact (closed)...

Des propriétés de finitude des foncteurs polynomiaux

Aurélien Djament (2016)

Fundamenta Mathematicae

We study finiteness properties, especially the noetherian property, the Krull dimension and a variation of finite presentation, in categories of polynomial functors (notion introduced by Djament and Vespa) from a small symmetric monoidal category whose unit is an initial object to an abelian category. We prove in particular that the category of polynomial functors from the category of free abelian groups ℤⁿ with split monomorphisms to abelian groups is "almost" locally noetherian. We also give an...

Matrix factorizations and singularity categories for stacks

Alexander Polishchuk, Arkady Vaintrob (2011)

Annales de l’institut Fourier

We study matrix factorizations of a potential W which is a section of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with potential W) with the singularity category of the zero locus of W generalizing a theorem of Orlov. We use this result to construct push-forward functors for matrix factorizations with relatively proper support.

Minimal resolutions and other minimal models.

Agustí Roig (1993)

Publicacions Matemàtiques

In many situations, minimal models are used as representatives of homotopy types. In this paper we state this fact as an equivalence of categories. This equivalence follows from an axiomatic definition of minimal objects. We see that this definition includes examples such as minimal resolutions of Eilenberg-Nakayama-Tate, minimal fiber spaces of Kan and Λ-minimal Λ-extensions of Halperin. For the first one, this is done by generalizing the construction of minimal resolutions of modules to complexes....

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