Methods of constructive category
                    theory

Posur, Sebastian

doi:10.1090/conm/769/15417

Cited by 3 publications

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“…The presented material follows closely the presentation of generalized morphisms given in [Pos17b], especially Subsections 2.2 and 2.3.…”

Section: Constructive Diagram Chasesmentioning

confidence: 88%

Methods of constructive category theory

Posur¹

2019

Preprint

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We give an introduction to constructive category theory by answering two guiding computational questions. The first question is: how do we compute the set of all natural transformations between two finitely presented functors like Ext and Tor over a commutative coherent ring R? We give an answer by introducing category constructors that enable us to build up a category which is both suited for performing explicit calculations and equivalent to the category of all finitely presented functors. The second question is: how do we determine the differentials on the pages of a spectral sequence associated to a filtered cochain complex only in terms of operations directly provided by the axioms of an abelian category? Its answer relies on a constructive method for performing diagram chases based on a calculus of relations within an arbitrary abelian category.

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“…The presented material follows closely the presentation of generalized morphisms given in [Pos17b], especially Subsections 2.2 and 2.3.…”

Section: Constructive Diagram Chasesmentioning

confidence: 88%

Methods of constructive category theory

Posur¹

2019

Preprint

Self Cite

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“…Significant progress in a functorial approach to the study of control systems was recently achieved by Sebastian Posur in [15], where he obtained a categorical framework for behaviors in algebraic system theory.…”

Section: Introductionmentioning

confidence: 99%

Injective stabilization of additive functors. II. (Co)torsion and the Auslander-Gruson-Jensen functor

Martsinkovsky

Russell

2020

Journal of Algebra

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Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture

Barakat

Kühne

2023

Math. Comp.

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In this paper, we show how to compute, using Fitting ideals, the nonfree locus of the moduli space of arrangements of a rank 3 3 simple matroid, i.e., the subset of all points of the moduli space which parametrize nonfree arrangements. Our approach relies on the so-called Ziegler restriction and Yoshinaga’s freeness criterion for multiarrangements. We use these computations to verify Terao’s freeness conjecture for rank 3 3 central arrangements with up to 14 14 hyperplanes in any characteristic.

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Methods of constructive category theory

Cited by 3 publications

References 0 publications

Methods of constructive category theory

Methods of constructive category theory

Injective stabilization of additive functors. II. (Co)torsion and the Auslander-Gruson-Jensen functor

Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture

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