Jekyll2023-01-24T09:56:27+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/Indec<p>New preprint.
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<p>Arxiv: <a href="https://arxiv.org/abs/2106.05798">https://arxiv.org/abs/2106.05798</a></p>
<p>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 <a href="https://arxiv.org/abs/2011.14758"><em>Khovanov-Sazdanovic’s recent generalizations of Deligne’s interpolation categories</em></a>.
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.</p>Sebastian PosurNew preprint.On 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-proving<p>New preprint.
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<p>Arxiv: <a href="https://arxiv.org/abs/2103.08379">https://arxiv.org/abs/2103.08379</a></p>
<p>Try out the corresponding <a href="https://github.com/sebastianpos/Adelman.jl">software</a>.</p>Sebastian PosurNew preprint.A 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-spaces<p>New preprint.
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<p>Arxiv: <a href="https://arxiv.org/abs/2003.13023">https://arxiv.org/abs/2003.13023</a></p>Sebastian PosurNew preprint.Closing 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-constructive<p>New preprint.
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<p>Arxiv: <a href="https://arxiv.org/abs/1911.11469">https://arxiv.org/abs/1911.11469</a></p>Sebastian PosurNew preprint.Tensor 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-functors<p>New preprint.
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<p>Arxiv: <a href="https://arxiv.org/abs/1909.00172">https://arxiv.org/abs/1909.00172</a></p>Sebastian PosurNew preprint.Methods Of Constructive Category Theory2019-08-15T00:00:00+02:002019-08-15T00:00:00+02:00https://sebastianpos.github.io/Methods-of-constructive-category-theory<p>New preprint.
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<p>Arxiv: <a href="https://arxiv.org/abs/1908.04132">https://arxiv.org/abs/1908.04132</a></p>Sebastian PosurNew preprint.Trying CAP in a Jupyter notebook2018-11-22T00:00:00+01:002018-11-22T00:00:00+01:00https://sebastianpos.github.io/Try-out-CAP<p>You can try CAP (Categories, Algorithms, Programming) in your browser
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running Jupyter notebooks interactively in Binder.</p>
<p>To start a CAP session with a worksheet on abelian categories, perform the following steps:</p>
<ol>
<li>
<p>Click on
<a href="https://mybinder.org/v2/gh/sebastianpos/cap-aachen2018/master"><img src="https://mybinder.org/badge.svg" alt="(Link to launch Binder)" /></a>
or open <a href="https://mybinder.org/v2/gh/sebastianpos/cap-aachen2018/master">https://mybinder.org/v2/gh/sebastianpos/cap-aachen2018/master</a> in the browser.</p>
</li>
<li>
<p>A message <code class="language-plaintext highlighter-rouge">Loading repository: sebastianpos/cap-aachen2018/master</code> 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.</p>
</li>
<li>
<p>Click on the <code class="language-plaintext highlighter-rouge">AbelianCategories.ipynb</code> file to start a Jupyter notebook on abelian categories.</p>
</li>
</ol>
<p>This worksheet was part of the <a href="https://homalg-project.github.io/capdays-2018/">CAP Days 2018</a>
at the University of Siegen
and the Summer School
<a href="https://lbfm-rwth.github.io/gap-in-algebraic-research-2018/">GAP in Algebraic Research</a>
at the RWTH Aachen.</p>Sebastian PosurYou can try CAP (Categories, Algorithms, Programming) in your browserAtom 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-geometry<p>New preprint.
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<p>Arxiv: <a href="https://arxiv.org/abs/1808.08792">https://arxiv.org/abs/1808.08792</a></p>Sebastian PosurNew preprint.CAP Days 20182018-09-10T00:00:00+02:002018-09-10T00:00:00+02:00https://sebastianpos.github.io/CAP-Days-2018_2<p>Thanks to all participants of the
<a href="https://homalg-project.github.io/capdays-2018/">CAP Days 2018</a>
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for the wonderful talks, the
eager participation in the CAP tutorials,
and the enhancements of
CAP during the coding sprint.</p>
<p><a href="https://homalg-project.github.io/capdays-2018/public/CapDays.JPG"><img src="https://homalg-project.github.io/capdays-2018/public/CapDaysThumb.JPG" alt="Group photo" title="Group photo" /></a></p>Sebastian PosurThanks to all participants of the CAP Days 2018CAP Days 20182018-02-07T00:00:00+01:002018-02-07T00:00:00+01:00https://sebastianpos.github.io/CAP-Days-2018<p>We are happy to announce CAP Days 2018, August 28 - August 31, at
University of Siegen.
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<p>Registration is possible at
<a href="https://homalg-project.github.io/capdays-2018/">https://homalg-project.github.io/capdays-2018/</a>.</p>
<p><a href="http://homalg-project.github.io/CAP_project">CAP (Categories, Algorithms, Programming)</a>
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.</p>
<p>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.</p>
<p>The workshop is split in three parts:</p>
<ul>
<li>Talks</li>
<li>Tutorial</li>
<li>Coding Sprint</li>
</ul>
<p>Best regards,</p>
<p>Sebastian Gutsche & Sebastian Posur</p>Sebastian PosurWe are happy to announce CAP Days 2018, August 28 - August 31, at University of Siegen.