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Let $B$ be a bialgebra, and $A$ a left $B$-comodule algebra in a braided monoidal category $\Cc$, and assume that $A$ is also a coalgebra, with a not-necessarily associative or unital left $B$-action...
Category computation theory deals with a web-based systemic processing that underlies the morphic webs, which constitute the basis of categorial logical calculus. It is proven that, for these structur...
Given a generic family $Q$ of 2-dimensional quadrics over a smooth 3-dimensional base $Y$ we consider the relative Fano scheme $M$ of lines of it. The scheme $M$ has a structure of a generically coni...
In this paper, we describe the irreducible representations in category O of the rational Cherednik algebra H_c(G_12,h) associated to the complex reflection group G_12 with reflection representation h ...
We prove an equivalence between the derived category of a variety and the equivariant/graded singularity category of a corresponding singular variety. The equivalence also holds at the dg level.
We consider the problem of enumerating permutations in the symmetric group on n elements which avoid a given set of consecutive pattern S, and in particular computing asymptotics as n tends to infin...
We consider the category of Deligne 1-motives over a perfect field k of exponential characteristic p and its derived category for a suitable exact structure after inverting p.
This study presents the taxonomy and threatened categories of 3 Achillea L. (Asteraceae-Anthemideae) species: A. membranacea (Labill.) DC., A. brachyphylla Boiss. & Hausskn., and A. boissieri Hausskn....
In this paper, we prove that there is a natural equivalence between the category ${\scr F}_1(x)$ of Koszul modules of complexity $1$ with filtration of given cyclic modules as the factor modules of an...
There are at least two kinds of generalization of Hopf algebra, i.e. pre-Hopf algebra and weak Hopf algebra. Correspondingly, we have two kinds of generalized bialgebras, almost bialgebra and weak bia...

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