Related papers: Abstract elementary classes and accessible categor…

We compute arithmetic Chern classes of sheaves on an arithmetic surface X associated to a Hermitian Azumaya algebra.

Writing parallel codes is difficult and exhibits a fundamental trade-off between abstraction and performance. The high level language abstractions designed to simplify the complexities of parallelism make certain assumptions that impacts…

Motivated by the free products of groups, the direct sums of modules, and Shelah's $(\lambda,2)$-goodness, we study strong amalgamation properties in Abstract Elementary Classes. Such a notion of amalgamation consists of a selection of…

We develop a 2-dimensional version of accessibility and presentability compatible with the formalism of flat pseudofunctors. First we give prerequisites on the different notions of 2-dimensional colimits, filteredness and cofinality; in…

For abelian length categories the borderline between finite and infinite representation type is discussed. Characterisations of finite representation type are extended to length categories of infinite height, and the minimal length…

We give a presentation in terms of generators and relations of Hopf algebras generated by skew-primitive elements and abelian group of group-like elements with action given via characters. This class of pointed Hopf algebras has shown great…

We explain our notion of a Nash geometric category, which allows an easy comparison between the following different axiomatic notions of geometric categories: o-minimal structures on the real field, analytic geometric categories and X-sets…

We present an intrinsic and concrete development of the subdivision of small categories, give some simple examples and derive its fundamental properties. As an application, we deduce an alternative way to compare the homotopy categories of…

For a Serre subcategory $\mathscr L$ and a resolving subcategory $\mathscr A$ of an abelian category, we show that the derived equivalence $D^b(\overline{\mathscr A} \cap \mathscr L) \simeq D^b_{\mathscr L}(\mathscr A)$ holds under certain…

We give a presentation theorem for continuous first-order logic and Metric Abstract Elementary classes in terms of $L_{\omega_1, \omega}$ and Abstract Elementary Classes, respectively. This presentation is accomplished by analyzing dense…

We provide a direct and elementary proof of the fact that the category of Nachbin's compact ordered spaces is dually equivalent to an Aleph_1-ary variety of algebras. Further, we show that Aleph_1 is a sharp bound: compact ordered spaces…

We study the equivalences induced by some special silting objects in the derived category over dg-algebra whose positive cohomologies are all zero.

We exhibit a categorical equivalence between the class of odd or even involutive FL$_e$-chains and a class of direct systems of abelian $o$-groups. Restricting this equivalence only to odd or only to even involutive FL$_e$-chains or to…

We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry.

We prove Koszulity of certain linear path categories obtained from connected graphs with some infinite directed walk. These categories can be viewed as locally quadratic dual to preprojective algebras.

We show that various tameness assertions about abstract elementary classes imply the existence of large cardinals under mild cardinal arithmetic assumptions.

We introduce notions of lax semiadditive and lax additive $(\infty,2)$-categories, categorifying the classical notions of semiadditive and additive 1-categories. To establish a well-behaved axiomatic framework, we develop a calculus of lax…

Explicit expression for quasi-triviality of scalar non-linear PDE is under consideration.

We interpret several constructions with C*-algebras as colimits in the bicategory of correspondences. This includes crossed products for actions of groups and crossed modules, Cuntz-Pimsner algebras of proper product systems, direct sums…

For an arbitrary affine Lie algebra we study an analog of the category O for the natural Borel subalgebra and zero central charge. We show that such category is semisimple having the reduced imaginary Verma modules as its simple objects.…