Jekyll2025-11-19T15:16:46+01:00https://sebastianpos.github.io/feed.xmlSebastian Posur - academic homepageacademic homepageSebastian PosurIndecomposable objects in Khovanov-Sazdanovic’s generalizations of Deligne’s interpolation categories2021-06-11T00:00:00+02:002021-06-11T00:00:00+02:00https://sebastianpos.github.io/IndecNew preprint.

Arxiv: https://arxiv.org/abs/2106.05798

We discuss categorical tools for the classification problem of indecomposable objects in Karoubian tensor categories. These tools include: filtrations, gradings, field extensions and Galois descent for such categories. We apply these tools to Khovanov-Sazdanovic’s recent generalizations of Deligne’s interpolation categories. Our chosen categorical point of view allows us to deduce results with a high level of generality: for example, we are able to determine the graded Grothendieck ring of Deligne’s interpolation categories over arbitrary fields, and the case of positive characterstic provides a natural setup for symmetric functions in the modular case.

]]>Sebastian PosurOn Free Abelian Categories For Theorem Proving2021-03-18T00:00:00+01:002021-03-18T00:00:00+01:00https://sebastianpos.github.io/On-free-abelian-categories-for-theorem-provingNew preprint.

Arxiv: https://arxiv.org/abs/2103.08379

Try out the corresponding software.

]]>Sebastian PosurA Constructive Approach To Fourier Mukai Transforms For Projective Spaces2020-03-29T00:00:00+01:002020-03-29T00:00:00+01:00https://sebastianpos.github.io/A-constructive-approach-to-Fourier-Mukai-transforms-for-projective-spacesNew preprint.

Arxiv: https://arxiv.org/abs/2003.13023

]]>Sebastian PosurClosing The Category Of Finitely Presented Functors Under Images Made Constructive2019-11-26T00:00:00+01:002019-11-26T00:00:00+01:00https://sebastianpos.github.io/Closing-the-category-of-finitely-presented-functors-under-images-made-constructiveNew preprint.

Arxiv: https://arxiv.org/abs/1911.11469

]]>Sebastian PosurTensor Products Of Finitely Presented Functors2019-08-31T00:00:00+02:002019-08-31T00:00:00+02:00https://sebastianpos.github.io/Tensor-products-of-finitely-presented-functorsNew preprint.

Arxiv: https://arxiv.org/abs/1909.00172

]]>Sebastian PosurMethods Of Constructive Category Theory2019-08-15T00:00:00+02:002019-08-15T00:00:00+02:00https://sebastianpos.github.io/Methods-of-constructive-category-theoryNew preprint.

Arxiv: https://arxiv.org/abs/1908.04132

]]>Sebastian PosurTrying CAP in a Jupyter notebook2018-11-22T00:00:00+01:002018-11-22T00:00:00+01:00https://sebastianpos.github.io/Try-out-CAPYou can try CAP (Categories, Algorithms, Programming) in your browser running Jupyter notebooks interactively in Binder.

To start a CAP session with a worksheet on abelian categories, perform the following steps:

  1. Click on (Link to launch Binder) or open https://mybinder.org/v2/gh/sebastianpos/cap-aachen2018/master in the browser.

  2. A message Loading repository: sebastianpos/cap-aachen2018/master will be displayed, followed by a non-interactive preview. Please be patient, since it may take a while, depending on the current load on Binder. When the server will be ready, you will see the main Jupyter screen with a file browser.

  3. Click on the AbelianCategories.ipynb file to start a Jupyter notebook on abelian categories.

This worksheet was part of the CAP Days 2018 at the University of Siegen and the Summer School GAP in Algebraic Research at the RWTH Aachen.

]]>Sebastian PosurAtom Spectra Of Graded Rings And Sheafification In Toric Geometry2018-09-10T00:00:00+02:002018-09-10T00:00:00+02:00https://sebastianpos.github.io/Atom-spectra-of-graded-rings-and-sheafification-in-toric-geometryNew preprint.

Arxiv: https://arxiv.org/abs/1808.08792

]]>Sebastian PosurCAP Days 20182018-09-10T00:00:00+02:002018-09-10T00:00:00+02:00https://sebastianpos.github.io/CAP-Days-2018_2Thanks to all participants of the CAP Days 2018 for the wonderful talks, the eager participation in the CAP tutorials, and the enhancements of CAP during the coding sprint.

Group photo

]]>Sebastian PosurCAP Days 20182018-02-07T00:00:00+01:002018-02-07T00:00:00+01:00https://sebastianpos.github.io/CAP-Days-2018We are happy to announce CAP Days 2018, August 28 - August 31, at University of Siegen.

Registration is possible at https://homalg-project.github.io/capdays-2018/.

CAP (Categories, Algorithms, Programming) is a software project for constructive category theory written in GAP. It facilitates both the realization of specific instances of categories and the implementation of generic categorical algorithms.

The workshop aims at mathematicians who want to learn about the CAP project, categorical programming, and structurizing implementations in a categorical way. The workshop is suitable for both GAP newcomers and veteran GAP programmers.

The workshop is split in three parts:

  • Talks
  • Tutorial
  • Coding Sprint

Best regards,

Sebastian Gutsche & Sebastian Posur

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