Related papers: Fibrations of algebras

Let X -> Y be a fibration whose fibers are complete intersections of two quadrics. We develop new categorical and algebraic tools---a theory of relative homological projective duality and the Morita invariance of the even Clifford algebra…

We construct a flagged $\infty$-category ${\sf Corr}$ of $\infty$-categories and bimodules among them. We prove that ${\sf Corr}$ classifies exponentiable fibrations. This representability of exponentiable fibrations extends that…

Let X be a smooth elliptic fibration over a smooth base B. Under mild assumptions, we establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an O^* gerbe over a genus one fibration which is a…

For a fibration with the fiber $K(\pi,n)$-space, the algebraic model as a twisted tensor product of chains of the base with standard chains of $K(\pi,n)$-complex is given which preserves multiplicative structure as well. In terms of this…

This survey is the continuation of a series of works aimed at applying tools from Singularity Theory to Differential Equations. More precisely, we utilize the powerfull Milnor's Fibration Theory to give geometric-topological classifications…

Suppose that f is a projective birational morphism with at most one-dimensional fibres between d-dimensional varieties X and Y, satisfying ${\bf R}f_* \mathcal{O}_X = \mathcal{O}_Y$. Consider the locus L in Y over which f is not an…

Let $X={\rm Spec}\: B$ be a factorial affine variety defined over an algebraically closed field $k$ of characteristic zero with a nontrivial action of the additive group $G_a$ associated to a locally nilpotent derivation $\delta$ on $B$.…

We note that large classes of contractions of algebras that arise in physics can be understood purely algebraically, via identifying appropriate $\mathbb{Z}_m$-gradings (and their generalizations) on the parent algebra. This includes…

We introduce a notion of extraction-contraction coproduct on twisted bialgebras, that is to say bialgebras in the category of linear species. If $P$ is a twisted bialgebra, a contraction-extraction coproduct sends $P[X]$ to…

We study several structure aspects of functor categories from a small additive category to a module category, in particular the category F(A,K) of functors from finitely generated free modules over a commutative ring A to vector spaces over…

Given a braided pivotal category $\mathcal C$ and a pivotal module tensor category $\mathcal M$, we define a functor $\mathrm{Tr}_{\mathcal C}:\mathcal M \to \mathcal C$, called the associated categorified trace. By a result of…

We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial…

We develop the theory of (op)fibrations of 2-multicategories and use it to define abstract six-functor-formalisms. We also give axioms for Wirthm\"uller and Grothendieck formalisms (where either $f^!=f^*$ or $f_!=f_*$) or intermediate…

Unstable operations in a generalized cohomology theory E give rise to a functor from the category of algebras over E to itself which is a colimit of representable functors and a comonoid with respect to composition of such functors. In this…

We investigate the connection between left exact $\infty$-functors between finitely complete quasicategories and exact functors between fibration categories, describing a procedure to approximate flat $\infty$-functors of the former type by…

In category theory, monads, which are monoid objects on endofunctors, play a central role closely related to adjunctions. Monads have been studied mostly in algebraic situations. In this dissertation, we study this concept in some…

In [arXiv:1509.02937], the notion of a module tensor category was introduced as a braided monoidal central functor $F\colon \mathcal{V}\longrightarrow \mathcal{T}$ from a braided monoidal category $\mathcal{V}$ to a monoidal category…

An $F$-zip over a scheme $S$ over a finite field is a certain object of semi-linear algebra consisting of a locally free module with a descending filtration and an ascending filtration and a $\Frob_q$-twisted isomorphism between the…

Suppose an extension map $U\colon \mathbb{T}_1 \to \mathbb{T}_0$ in the 2-category $\mathfrak{Con}$ of contexts for arithmetic universes satisfies a Chevalley criterion for being an (op)fibration in $\mathfrak{Con}$. If $M$ is a model of…

Let $f : X -> B$ be a projective surjective morphism between quasi-projective varieties. The goal of this paper is the study of the Chow groups of $X$ in terms of the Chow groups of $B$ and of the fibers of $f$. One of the applications…