Related papers: Krull-Schmidt categories and projective covers
Given a category $\mathcal C$ and a directed partially ordered set $J$, a certain category $pro^J -\mathcal C$ on inverse systems in $\mathcal C$ is constructed such that the ordinary pro-category $pro-\mathcal C$ is the most special case…
We define special objects, Ulrich objects, on a derived category of polarized smooth projective variety as a generalization of Ulrich bundles to the derived category. These are defined by the cohomological conditions that are the same form…
We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general…
We provide a technique to glue simple-minded collections along a recollement of Hom-finite Krull-Schmidt triangulated categories over a field. This gluing technique for simple-minded collections is shown to be compatible with those for…
The present work develops a construction of a CD category of partial kernels from a particular type of Markov category called a partializable Markov category. These are a generalization of earlier models of categories of partial morphisms…
Inverse categories are categories in which every morphism x has a unique pseudo-inverse y in the sense that xyx=x and yxy=y. Persistence modules from topological data analysis and similarly decomposable category representations factor…
In this paper we introduce the concept of inflexible $CR$ submanifolds. These are $CR$ submanifolds of some complex Euclidean space such that any compactly supported $CR$ deformation is again globally $CR$ embeddable into some complex…
We construct a relative Chow-Kunneth decomposition for a conic bundle over a surface such that the middle projector gives the Prym variety of the associated double covering of the discriminant of the conic bundle. This gives a refinement…
In this paper we define quadratic categories and their representations.
We classify C$^*$ near-group categories by using Vaughan Jones theory of subfactors and the Cuntz algebra endomorphisms. Our results show that there is a sharp contrast between two essentially different cases, integral and irrational cases.…
In a previous work we constructed the $Q$-shaped derived category of any ring $A$ for any suitably nice category $Q$. The $Q$-shaped derived category of $A$, which is denoted by $\mathcal{D}_{Q}(A)$, is a generalization of the ordinary…
An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…
The famous Burnside-Schur theorem states that every primitive finite permutation group containing a regular cyclic subgroup is either 2-transitive or isomorphic to a subgroup of a 1-dimensional affine group of prime degree. It is known that…
Assume that $K$ is an algebraically closed field, $R$ a locally support-finite locally bounded $K$-category, $G$ a torsion-free admissible group of $K$-linear automorphisms of $R$ and $A=R/G$. We show that the Krull-Gabriel dimension…
Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous…
Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f in Int(D), we explicitly construct a divisor homomorphism from [f], the divisor-closed submonoid of Int(D) generated by f, to a finite sum of copies…
From a bimodule $M$ over an exact category $C$, we define an exact category $C\ltimes M$ with a projection down to $C$. This construction classifies certain split square zero extensions of exact categories. We show that the trace map…
The multipullback quantization of complex projective spaces lacks the naive quantum CW-complex structure because the quantization of an embedding of the $n$-skeleton into the $(n+1)$-skeleton does not exist. To overcome this difficulty, we…
The restriction of a supercuspidal representation of SL_2(k), for k a local nonarchimedean field, to a maximal compact subgroup decomposes as a multiplicity-free direct sum of irreducible representations. We explicitly describe this…
By introducing a notion of smooth connection for unbounded $KK$-cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order to achieve this it is necessary to develop a framework of…