We interpret the complexes defining rack cohomology in terms of a certain differential graded bialgebra. This yields elementary algebraic proofs old and new structural results for this theory. For instance, we exhibit two explicit homotopies controlling structure defects on cochain level: one commutativity defect cup product, other "Zinbielity" dendriform structure. also show that, quandle, pro...

Let LM denote the coproduct of the bounded distributive lattices L and M. At the 1981 Bann Conference on Ordered Sets, the following question was posed: What is the largest class L of nite distributive lattices such that, for every non-trivial Boolean lattice B and every L 2 L, B L = B L 0 implies L = L 0 ? In this note, the problem is solved.

We describe and study a four parameters deformation of the two products and the coproduct of the Hopf algebra of plane posets. We obtain a family of braided Hopf algebras, which are generically self-dual. We also prove that in a particular case (when the second parameter goes to zero and the first and third parameters are equal), this deformation is isomorphic, as a self-dual braided Hopf algeb...

Abstract In this study, mainly, we introduce the category Tex of textures and texturally continuous functions. Relations with some other categories, particulary dfTex, fTex, are pointed out. It is shown that the categories CTop of C-spaces and a full subcategory of Sober of sober spaces are, respectively, isomorphic to Tex and STex of simple textures. Some properties discussed including the exi...

We introduce λμ→∧∨⊥, an extension of Parigot’s λμ-calculus where disjunction is taken as a primitive. The associated reduction relation, which includes the permutative conversions related to disjunction, is Church-Rosser, strongly normalizing, and such that the normal deductions satisfy the subformula property. From a computer science point of view, λμ→∧∨⊥ may be seen as the core of a typed cbn...

We consider the extensions of classical r-matrix for κ-deformed Poincaré algebra which satisfy modified Yang-Baxter equation. Two examples introducing additional deformation parameter (dimension-full 1 κ or dimensionless ξ) are presented. We describe the corresponding quantization (two-parameter κ-Poincaré quantum Hopf algebras) in explicite form as obtained by twisting of standard κ-deformed f...

Abstract. We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally cartesian closed category, whereas the additive (product and coproduct) and exponential (⊗-comonoid comonad) structures require additional properties and a...

It is our purpose here to announce the results of our study of the homology of the spaces in the £2-spectrum for complex cobordism and BrownPeterson cohomology. Let MU(n) be the standard Thorn complex. MUk = l im^^ ü,(~~)MU(n) is the 2k space in the £2-spectrum for complex cobordism. We will consider the space MU — hmn^_00 Iï ;>n MUf-. We find this product easier to study than the separate fact...

We begin by considering the graded vector space with a basis consisting of rooted trees, with grading given by the count of non-root vertices. We define two linear operators on this vector space, the growth and pruning operators, which respectively raise and lower grading; their commutator is the operator that multiplies a rooted tree by its number of vertices, and each operator naturally assoc...

Sirtuins are protein deacetylases regulating metabolism and stress responses. The seven human Sirtuins (Sirt1-7) are attractive drug targets, but Sirtuin inhibition mechanisms are mostly unidentified. We report the molecular mechanism of Sirtuin inhibition by 6-chloro-2,3,4,9-tetrahydro-1H-carbazole-1-carboxamide (Ex-527). Inhibitor binding to potently inhibited Sirt1 and Thermotoga maritima Si...