nLab Martin Brandenburg

• Mathematics Genealogy page

Selected writings

Publications

• Algebraic games – playing with groups and rings, International Journal of Game Theory, 47, 417–450(2018), arXiv

• Operations on categories of modules are given by Schur functors, Applied Categorical Structures, 26, 287–308(2018), arXiv

• Rosenberg’s reconstruction theorem (after Gabber), Expositiones Mathematicae, Volume 36, Issue 1, March 2018, Pages 98-117, arXiv

• with A. Chirvasitu and T. Johnson-Freyd, Reflexivity and dualizability in categorified linear algebra, Theory and Applications of Categories 30 (2015), No. 23, 808-835, arXiv

• with A. Chirvasitu, Tensor functors between categories of quasi-coherent sheaves, Journal of Algebra 399 (2014), 675-692, arXiv

Books

On category theory:

• Einführung in die Kategorientheorie: Mit ausführlichen Erklärungen und zahlreichen Beispielen, Second edition, Springer, 2016.

Preprints

On ring theory:

• Equational proofs of Jacobson’s Theorem, 2023, arxiv

On Galois theory:

• A simple proof of the fundamental theorem of Galois theory, 2022, arxiv

On limit sketches:

• Large limit sketches and topological space objects, 2021, arXiv

On localization of tensor categories

• Localizations of tensor categories and fiber products of schemes, 2020, arXiv

On 2-limits of tensor categories:

• Bicategorical colimits of tensor categories, 2020, arXiv

On tensor category-theory for algebraic geometry:

• Tensor categorical foundations of algebraic geometry, PhD thesis, University of Münster, 2014, arXiv

  Errata for PhD thesis: The reflectors in 5.8.17, 5.8.18, 5.8.20, 5.8.21, 5.10.6 are not correct in general and should be removed.