Related papers: Adjointness properties for relative extensions of …

We study varieties generated by semi-primal lattice-expansions by means of category theory. We provide a new proof of the Keimel-Werner topological duality for such varieties and, using similar methods, establish its discrete version. We…

Let $f \colon X \to Y$ be a morphism of concentrated schemes. We characterize $f$-perfect complexes $\mathcal{E}$ as those such that the functor $\mathcal{E} \otimes^{\mathbf{L}}_X \mathbf{L} f^*-$ preserves bounded complexes. We prove, as…

We introduce the concept of Hom-associative algebra structures in Loday-Pirashvili category.The cohomology theory of Hom-associative algebras in this category is studied.Some applications on deformation and abelian extension theory are…

In this paper, we show the relation among the relative central extensions in an isoclinism family of a particular relative central extension of Hom-Lie algebras. We define the notion of isoclinism on the central relative extensions of a…

We study the homological algebra in the category $\mathcal{P}_p$ of strict polynomial functors of degree $p$ over a field of positive characteristic $p$. We determine the decomposition matrix of our category and we calculate the Ext-groups…

Let $\mathcal C$ be category over a commutative ring $k$, its Hochschild-Mitchell homology and cohomology are denoted respectively $HH_*(\mathcal C)$ and $HH^*(\mathcal C).$ Let $G$ be a group acting on $\mathcal C$, and $\mathcal C[G]$ be…

Much of the homotopical and homological structure of the categories of chain complexes and topological spaces can be deduced from the existence and properties of the 'simple' functors Tot : {double chain complexes} -> {chain complexes} and…

Let $\mathcal{C}$ be a small category, $\mathfrak{A}$ be a precosheaf of unital $k$-algebras on $\mathcal{C}$ and $\mathfrak{M}$ be an $\mathfrak{A}$-bimodule. We introduce two new notions, namely, the Grothendieck construction…

We introduce a bialgebra axiom for a pair $(c,\ell)$ of a colax-monoidal and a lax-monoidal structures on a functor $F\colon \mathscr{M}_1\to \mathscr{M}_2$ between two (strict) symmetric monoidal categories. This axiom can be regarded as a…

In this thesis we develop the cohomology of diagrams of algebras and then apply this to the cases of the $\lambda$-rings and the $\Psi$-rings. A diagram of algebras is a functor from a small category to some category of algebras. For an…

Let $k$ be a regular ring, and let $A,B$ be essentially finite type $k$-algebras. For any functor $F:{D}(A)\times\dots\times{D}(A)\to{D}(B)$ between their derived categories, we define its twist…

Auslander-Reiten duality for module categories is generalised to Grothendieck abelian categories that have a sufficient supply of finitely presented objects. It is shown that Auslander-Reiten duality amounts to the fact that the functor…

We develop the theory of the intertwining distributional versions of the LS-category and the sequential topological complexities of a space $X$, denoted by $\mathsf{icat}(X)$ and $\mathsf{iTC}_m(X)$, respectively. We prove that they satisfy…

We demonstrate that companionships and conjunctions in double $\infty$-categories -- and more generally, in double Segal spaces -- extend to functors out of the free-living companionship and conjunction respectively. Specifically, we prove…

On an open, connected symplectic manifold $(M,\omega)$, the group of Hamiltonian diffeomorphisms forms an infinite-dimensional Fr\'echet Lie group with Lie algebra $C^{\infty}_c(M)$ and adjoint action given by pullbacks. We prove that this…

In this paper, we consider homology groups induced by the exterior algebra generated by a simplicial compliment of a simplicial complex $K$. These homology groups are isomorphic to the Tor-groups $\mathrm{Tor}_{i,…

Let $D_j\subset\Bbb C^{k_j}$ be a pseudoconvex domain and let $A_j\subset D_j$ be a locally pluripolar set, $j=1,...,N$. Put$$X:=\bigcup_{j=1}^N A_1\times...\times A_{j-1}\times D_j\times A_{j+1}\times...\times A_N\subset\Bbb…

For a locally compact group $G$, let $A^n(G)$ denote the multidimensional Fourier algebra given by $ \otimes_{n}^{eh} A(G).$ This work explores the approximation identity and operator amenability of the algebra $A^n(G)$. Further, we study…

Let $(G,N)$ be a pair of groups. In this article, first we construct a relative central extension for the pair $(G,N)$ such that special types of covering pair of $(G,N)$ are homomorphic image of it. Second, we show that every perfect pair…

For any additive functor from modules (or, more generally, from an abelian category with enough projectives or injectives), we construct long sequences tying up together the derived functors, the satellites, and the stabilizations of the…