Related papers: Enriched pro-categories and shapes

A theory of characteristic classes of vector bundles and smooth manifolds plays an important role in the theory of smooth manifolds. An investigation of reasonable notions of characteristic classes of singular spaces started since a…

Knop constructed a tensor category associated to a finitely-powered regular category equipped with a degree function. In recent work with Harman, we constructed a tensor category associated to an oligomorphic group equipped with a measure.…

We prove the functoriality for proper push-forward of the characteristic cycles of constructible complexes by morphisms of smooth projective schemes over a perfect field, under the assumption that the direct image of the singular support…

Enriched categories are categories whose sets of morphisms are enriched with extra structure. Such categories play a prominent role in the study of higher categories, homotopy theory, and the semantics of programming languages. In this…

Let $\mathcal C$ be the category of finite graphs. Lov\`{a}sz shows that the semi-ring of isomorphism classes of $\mathcal C$ (with coproduct as sum, and product as multiplication) is embedded into the direct product of the semi-ring of…

We give a classification theorem for a class of C*-algebras which are direct limits of extensions of circle algebras by purely infinite C*-algebras. The invariant consists of the following: (1) the set of Murray-von Neumann equivalence…

We further the theory of optics or "circuits-with-holes" to encompass premonoidal categories: monoidal categories without the interchange law. Every premonoidal category gives rise to an effectful category (i.e. a generalised…

We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…

We consider and characterize classes of finite and countably categorical structures and their theories preserved under $E$-operators and $P$-operators. We describe $e$-spectra and families of finite cardinalities for structures belonging to…

Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A…

Let {\cal T} be a triangulated category, {\cal A} a full subcategory of {\cal T} and {\cal X} a functorially finite subcategory of {\cal A}. If {\cal A} has the properties that any {\cal X}-monomorphism of {\cal A} has a cone and any {\cal…

We associate a rational number $\chi(\mathcal{A})$ to every category $\mathcal{A}$ whose object and morphism sets are finite. We show that the assignment $\chi$ is additive under disjoint union and it preserves products. Hence we consider…

It has been proven by Schupp and Bergman that the inner automorphisms of groups can be characterized purely categorically as those group automorphisms that can be coherently extended along any outgoing homomorphism. One is thus motivated to…

We study the Farrell-Jones Conjecture with coefficients in an additive G-category with involution. This is a variant of the L-theoretic Farrell-Jones Conjecture which originally deals with group rings with the standard involution. We show…

Let $\Mod \CS$ denote the category of $\CS$-modules, where $\CS$ is a small category. In the first part of this paper, we provide a version of Rickard's theorem on derived equivalence of rings for $\Mod \CS$. This will have several…

We relate the theory of purity of a locally finitely presented category with products to the study of exact structures on the full subcategory of finitely presented objects. Properties in the context of purity are translated to properties…

A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. In \cite{DR2} we gave characterizations of monomorphisms (resp. epimorphisms) in arbitrary pro-categories, pro-(C), where (C) has…

Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.

We prove a topological version of the section conjecture for the profinite completion of the fundamental group of finite CW-complexes equipped with the action of a group of prime order $p$ whose $p$-torsion cohomology can be killed by…

We define the affinization of an arbitrary monoidal category $\mathcal{C}$, corresponding to the category of $\mathcal{C}$-diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to…