28 citations · 59 across the 11 of their papers we have counts for
12 papers
Equational proofs of Jacobson's Theorem
Martin Brandenburg
A classical theorem by Jacobson says that a ring in which every element satisfies the equation for some is commutative. According to Birkhoff's Completeness Theor…
A simple proof of the fundamental theorem of Galois theory
Martin Brandenburg
We present a simple proof of the fundamental theorem of Galois theory, which establishes a correspondence between the intermediate fields of a finite Galois extension and the subgr…
Large limit sketches and topological space objects
Martin Brandenburg
For a (possibly large) realized limit sketch such that every -model is small in a suitable sense we show that the category of cocontinuous functors $\mat…
Localizations of tensor categories and fiber products of schemes
Martin Brandenburg
We prove that the tensor category of quasi-coherent modules on a fiber product of quasi-compact quasi-separated schemes is the bicategorical pushout o…
Bicategorical colimits of tensor categories
Martin Brandenburg
In this expository paper we explain in detail how to construct bicategorical colimits of several kinds of tensor categories, for example essentially small finitely cocomplete K-lin…
Operations on categories of modules are given by Schur functors
Martin Brandenburg
Let be a commutative -algebra. We study families of functors between categories of finitely generated -modules which are defined for all commutative -algebras…
Tensor categorical foundations of algebraic geometry
Martin Brandenburg
Tannaka duality and its extensions by Lurie, Schäppi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sh…
Reflexivity and dualizability in categorified linear algebra
Martin Brandenburg, Alexandru Chirvasitu, Theo Johnson-Freyd
The "linear dual" of a cocomplete linear category is the category of all cocontinuous linear functors . We study the questions of when a…
Rosenberg's Reconstruction Theorem (after Gabber)
Martin Brandenburg
Alexander L. Rosenberg has constructed a spectrum for abelian categories which is able to reconstruct a quasi-separated scheme from its abelian category of quasi-coherent sheaves.…
Algebraic games - Playing with groups and rings
Martin Brandenburg
Two players alternate moves in the following impartial combinatorial game: Given a finitely generated abelian group , a move consists of picking some nonzero element .…
Tensor functors between categories of quasi-coherent sheaves
Martin Brandenburg, Alexandru Chirvasitu
For a quasi-compact quasi-separated scheme X and an arbitrary scheme Y we show that the pullback construction implements an equivalence between the discrete category of morphisms Y…
Tensorial schemes
Martin Brandenburg
Jacob Lurie (arXiv:math/0412266) has shown that for geometric stacks X,Y every cocontinuous tensor functor F : Qcoh(X) -> Qcoh(Y) is the pullback of a morphism Y -> X under the add…