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Making factorizations compositive

Reinhard Börger (1991)

Commentationes Mathematicae Universitatis Carolinae

The main aim of this paper is to obtain compositive cone factorizations from non-compositive ones by itereration. This is possible if and only if certain colimits of (possibly large) chains exist. In particular, we show that (strong-epi, mono) factorizations of cones exist if and only if joint coequalizers and colimits of chains of regular epimorphisms exist.

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.

Metric enrichment, finite generation, and the path coreflection

Alexandru Chirvasitu (2024)

Archivum Mathematicum

We prove a number of results involving categories enriched over CMet, the category of complete metric spaces with possibly infinite distances. The category CPMet of path complete metric spaces is locally 1 -presentable, closed monoidal, and coreflective in CMet. We also prove that the category CCMet of convex complete metric spaces is not closed monoidal and characterize the isometry- 0 -generated objects in CMet, CPMet and CCMet, answering questions by Di Liberti and Rosický. Other results include...

Minimal finite models.

Barmak, Jonathan Ariel, Minian, Elias Gabriel (2007)

Journal of Homotopy and Related Structures

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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