Related papers: An algebraic model for commutative HZ-algebras
In a recent paper, the authors introduced the notion of an alternating snake and a corresponding family of finite dimensional modules for the quantum affine algebra associated to $A_n$. We prove that under some restrictions, an alternating…
The purpose of this paper is to develop a homotopical algebra for graphs, relevant to zeta series and spectra of finite graphs. More precisely, we define a Quillen model structure in a category of graphs (directed and possibly infinite,…
Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…
We construct a "diagonal" cofibrantly generated model structre on the category of simplicial objects in the category of topological categories sCat_{Top}, which is the category of diagrams [\Delta^{op}, Cat_{Top}]. Moreover, we prove that…
We prove that commutative semirings in a cartesian closed presentable $\infty$-category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product-preserving functors from the $(2,1)$-category of bispans of finite sets. In other…
We establish a highly flexible condition that guarantees that all colored symmetric operads in a symmetric monoidal model category are admissible, i.e., the category of algebras over any operad admits a model structure transferred from the…
It is well known that very special $\Gamma$-spaces and grouplike $\E_\infty$ spaces both model connective spectra. Both these models have equivariant analogues. Shimakawa defined the category of equivariant $\Gamma$-spaces and showed that…
If a Quillen model category can be specified using a certain logical syntax (intuitively, ``is algebraic/combinatorial enough''), so that it can be defined in any category of sheaves, then the satisfaction of Quillen's axioms over any site…
Building on structure observed in equivariant homotopy theory, we define an equivariant generalization of a symmetric monoidal category: a $G$-symmetric monoidal category. These record not only the symmetric monoidal products but also…
We assign a relational structure to any finite algebra in a canonical way, using solution sets of equations, and we prove that this relational structure is polymorphism-homogeneous if and only if the algebra itself is…
We associate a monoidal category $\mathcal{H}^\lambda$ to each dominant integral weight $\lambda$ of $\widehat{\mathfrak{sl}}_p$ or $\mathfrak{sl}_\infty$. These categories, defined in terms of planar diagrams, act naturally on categories…
If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit S forms a commutative ring. An idempotent e of this ring will split the homotopy category. We prove that provided the…
In this article the author endows the functor category [B(Z2),Gpd] with the structure of a type-theoretic fibration category with a univalent universe using the so-called injective model structure. It gives us a new model of Martin-L\"of…
In his fundamental work, Quillen developed the theory of the cotangent complex as a universal abelian derived invariant, and used it to define and study a canonical form of cohomology, encompassing many known cohomology theories. Additional…
The paper is devoted to study the space of multiplicative maps from the Eilenberg-MacLane spectrum $H\Z$ to an arbitrary ring spectrum $R$. We try to generalize the approach of Schwede from "Formal groups and stable homotopy of commutative…
We relate two different proposals to extend the \'etale topology into homotopy theory, namely via the notion of finite cover introduced by Mathew and via the notion of separable commutative algebra introduced by Balmer. We show that finite…
We give a homotopy theoretic characterization of stacks on a site $\cC$ as the {\it homotopy sheaves} of groupoids on $\cC$. We use this characterization to construct a model category in which stacks are the fibrant objects. We compare…
Green's theorem states that the Hall algebra of the category of representations of a quiver over a finite field is a twisted bialgebra. Considering instead categories of orthogonal or symplectic quiver representations leads to a class of…
This work develops a comprehensive algebraic model for rational stable parametrized homotopy theory over arbitrary base spaces. Building on the simplicial analogue of the foundational framework of May-Sigurdsson for parametrized spectra,…
We study the homotopy category $ K(\Inj A)$ of all injective modules over a finite dimensional algebra $A$ with discrete derived category. We give a classification of the indecomposable objects of $ K(\Inj A)$ for any radical square zero…