Related papers: Dold-Kan correspondence for dendroidal abelian gro…

We prove that if two abelian varieties have equivalent derived categories then the derived categories of the smooth stacks associated to the corresponding Kummer varieties are equivalent as well. The second main result establishes necessary…

We show that weak monoidal Quillen equivalences induce equivalences of symmetric monoidal $\infty$-categories with respect to the Dwyer-Kan localization of the symmetric monoidal model categories. The result will induce a Dold-Kan…

We provide examples of inductive fibrant replacements in fibrantly generated model categories constructed as Postnikov towers. These provide new types of arguments to compute homotopy limits in model categories. We provide examples for…

We establish a canonical correspondence between connected quandles and certain configurations in transitive groups, called quandle envelopes. This correspondence allows us to efficiently enumerate connected quandles of small orders, and…

Homology is characterized by the Eilenberg-Steenrod axioms. We define homology of higher categories via a categorical analogue of the Eilenberg-Steenrod axioms. We prove a categorical Dold-Kan correspondence, providing a combinatorial…

We give a simple proof for the rigidity of a complex in the bounded derived category of sheaves with constructible cohomology on an abelian variety.

We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…

The monoidal properties of the Dold-Kan correspondence have been studied in homotopy theory, notably by Schwede and Shipley. Changing the enrichment of an enriched, tensored, and cotensored category along the Dold-Kan correspondence does…

For an abelian category, a category equivalent to its derived category is constructed by means of specific projective (injective) multicomplexes, the so-called homological resolutions.

This work originates from chapters V and VII of Grothendieck's manuscript Pursuing Stacks, which contains a series of questions, as well as a previously unexplored formalism, concerning the interactions between the notion of test categories…

By a theorem of Christensen and Hovey, the category of non-negatively graded chain complexes has a model structure, called the h-model structure or Hurewicz model structure, where the weak equivalences are the chain homotopy equivalences.…

We introduce $n$-abelian and $n$-exact categories, these are analogs of abelian and exact categories from the point of view of higher homological algebra. We show that $n$-cluster-tilting subcategories of abelian (resp. exact) categories…

Building on work of Derksen-Fei and Plamondon, we formulate a conjectural correspondence between additive and monoidal categorifications of cluster algebras, which reveals a new connection between the additive reachability conjecture and…

A version of Dwyer-Kan localization in the context of infinity-categories and simplicial categories is presented. Some results of the classical papers by Dwyer and Kan on simplicial localization are reproven and generalized. It is proven…

An extension of order theory is presented that serves as a formalism for the study of dendroidal sets analogously to way the formalism of order theory is used in the study of simplicial sets.

We show that the bicategory of proper correspondences is the Dwyer-Kan localisation of the category of C*-algebras at a certain class of *-homomorphisms.

We prove that for certain monoidal (Quillen) model categories, the category of comonoids therein also admits a model structure.

We compute the Grothendieck group of the category of abelian varieties over an algebraically closed field $k$. We also compute the Grothendieck group of the category of $A$-isotypic abelian varieties, for any simple abelian variety $A$,…

This note gives a one-to-one correspondence between the equivalence classes of a certain type of 2-dimensional Calabi-Yau categories, and certain type of quivers, This is an analogue of the result in Stability structures, motivic…

Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective…