This is the second in a series on configurations in an abelian category A. Given a finite poset
(I,≼), an (I,≼)-configuration (σ, ι, π) is a finite collection of objects σ (J) and morphisms ι (J, K) …

We show that the categories of magmas, of semigroups, of magmas with identity, of
monoids, of groups, of rings, and of commutative rings, admit no monoidal biclosed …

arXiv:2305.11303v1 [math.CT] 18 May 2023 Page 1 arXiv:2305.11303v1 [math.CT] 18 May
2023 Dilatations of categories Arnaud Mayeux May 22, 2023 Abstract. This note unifies, in the …

This is a foundation for algebraic geometry, developed internal to the Zariski topos, building
on the work of Kock and Blechschmidt ([Koc06][I. 12],[Ble17]). The Zariski topos consists of …

For a commutative ring $ R $, we exploit localization techniques and point-free topology to
give an explicit realization of both the Zariski frame of $ R $(the frame of radical ideals in $ R …

This chapter describes interrelations between:(1) algebraic structure on sets of scalars,(2)
properties of monads associated with such sets of scalars, and (3) structure in categories …

We show that, over an arbitrary commutative ring, the localizations of the categories of dg
categories, of unital and of strictly unital $ A_\infty $ categories with respect to the …

A natural question in the theory of Tannakian categories is: What if you don't remember
Forget? Working over an arbitrary commutative ring R, we prove that an answer to this …

Let∗ be a star operation of finite character. Call a∗-ideal I of finite type a∗-homogeneous
ideal if I is contained in a unique maximal∗-ideal M= M (I). A maximal∗-ideal that contains …

We prove a Tannaka duality theorem for (∞, 1)-categories. This is a duality between certain
derived group stacks, or more generally certain derived gerbes, and symmetric monoidal …