Abstract
AbstractSuppose that we have a bicomplete closed symmetric monoidal quasi-abelian category $$\mathcal {E}$$
E
with enough flat projectives, such as the category of complete bornological spaces $${{\textbf {CBorn}}}_k$$
CBorn
k
or the category of inductive limits of Banach spaces $${{\textbf {IndBan}}}_k$$
IndBan
k
. Working with monoids in $$\mathcal {E}$$
E
, we can generalise and extend the Koszul duality theory of Beilinson, Ginzburg, Soergel. We use an element-free approach to define the notions of Koszul monoids, and quadratic monoids and their duals. Schneiders’ embedding of a quasi-abelian category into an abelian category, its left heart, allows us to prove an equivalence of certain subcategories of the derived categories of graded modules over Koszul monoids and their duals.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
General Computer Science,Theoretical Computer Science,Algebra and Number Theory
Reference24 articles.
1. Bambozzi, F., Ben-Bassat, O.: Dagger geometry as Banach algebraic geometry. J. Number Theory 162, 391–462 (2016)
2. Bambozzi, F., Ben-Bassat, O., Kremnizer, K.: Stein domains in Banach algebraic geometry. J. Funct. Anal. 274, 1865–1927 (2018)
3. Bambozzi, F., Kremnizer, K.: On the sheafyness property of spectra of Banach rings (2020). Arxiv e-prints ArXiv:2009.13926v2
4. Beilinson, A., Ginzburg, V., Soergel, W.: Koszul duality patterns in representation theory. J. Am. Math. Soc. 9(2), 473–527 (1996)
5. Ben-Bassat, O., Kremnizer, K.: Non-Archimedean analytic geometry as relative algebraic geometry. Annales de la faculté des sciences de Toulouse Mathématiques, XXV I(1), 49–126 (2017)