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HOPF MONOIDS IN THE CATEGORY OF SPECIES
Species Hopf monoid Lie monoid antipode Hadamard product
2015/8/14
A Hopf monoid (in Joyal’s category of species) is an algebraic
structure akin to that of a Hopf algebra. We provide a self-contained introduction
to the theory of Hopf monoids in the category of spe...
Existence, uniqueness, universality and functoriality of the perfect locality over a Frobenius P-category
Existence functoriality of the perfect locality Frobenius P-category Group Theory
2012/7/9
Let p be a prime, P a finite p-group and F a Frobenius P-category. The question on the existence of a suitable category L^sc extending the full subcategory of F over the set of F-selfcentralizing subg...
On the derived category of the classical Godeaux surface
the derived category the classical Godeaux surface Algebraic Geometry
2012/6/30
We construct an exceptional sequence of length 11 on the classical Godeaux surface X which is the Z/5-quotient of the Fermat quintic surface in P^3. This is the maximal possible length of such a seque...
On Lusternik-Schnirelmann Category of Connected Sums
Lusternik-Schnirelmann Category of Connected Sums Algebraic Topology
2012/5/9
In this paper we estimate the Lusternik-Schnirelmann category of the connected sum of two manifolds through their categories. We achieve a more general result regarding the category of a quotient spac...
Twisted split category algebras as quasi-hereditary algebras
Group Theory category algebras quasi-hereditary algebras
2012/4/16
A category is called {\em split} if for every morphism $s\colon X\to Y$ there exists a morphism $t\colon Y\to X$ such that $s\circ t\circ s = s$. Let $C$ be a finite split category, let $k$ be a field...
Finite generators for countable group actions in the Borel and Baire category settings
Finite generators countable group actions Baire category settings Logic
2012/4/23
For a countable group G and a standard Borel G-space X, a countable Borel partition P of X is called a generator if {gA : g in G, A in P} generates the Borel sigma-algebra of X. For G=Z, the Kolmogoro...
Not every object in the derived category of a ring is Bousfield equivalent to a module
Not every object derived category ring Bousfield equivalent module
2012/3/1
We consider the derived category of a specific non-Noetherian ring \Lambda, and show that there are objects in D(\Lambda) that are not Bousfield equivalent to any module. This answers a question posed...
The Brauer-Picard group of the representation category of finite supergroup algebras
Brauer-Picard group tensor category module category Quantum Algebra
2012/2/29
We develop further the techniques presented in [M. Mombelli. On the tensor product of bimodule categories over Hopf algebras. Preprint arXiv:1111.1610 ] to study bimodule categories over the represent...
Category O for Rational Cherednik Algebras H_{t,c}(GL_2(F_p),h) in Characteristic p
Rational Cherednik Algebras Characteristic p Representation Theory
2011/9/23
Abstract: In this paper we describe the characters of irreducible objects in category O for the rational Cherednik algebra associated to GL_2(F_p) over an algebraically closed field of positive charac...
On the derived category of a graded commutative noetherian ring
Localizing subcategories graded ring weighted projective scheme
2011/9/20
Abstract: For any graded commutative noetherian ring, where the grading group is abelian and where commutativity is allowed to hold in a quite general sense, we establish an inclusion-preserving bijec...
Category equivalences involving graded modules over path algebras of quivers
Category equivalences path algebras of quivers Rings and Algebras
2011/9/14
Abstract: Let kQ be the path algebra of a quiver Q with its standard grading. We show that the category of graded kQ-modules modulo those that are the sum of their finite dimensional submodules, QGr(k...
Convex hyperspaces of probability measures and extensors in the asymptotic category
Compact convex set probability measure asymptotically zero-dimensional space absolute extensor
2011/8/26
Abstract: The objects of the Dranishnikov asymptotic category are proper metric spaces and the morphisms are asymptotically Lipschitz maps. In this paper we provide an example of an asymptotically zer...
Logarithmic tensor category theory, VI: Expansion condition, associativity of logarithmic intertwining operators, and the associativity isomorphisms
Logarithmic tensor category theory, VI: Expansion condition associativity of logarithmic intertwining operators associativity isomorphisms
2011/2/23
This is the sixth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (...
In the category of relative categories the Rezk equivalences are exactly the DK-equivalences
category of relative categories Rezk equivalences exactly the DK-equivalences
2011/1/19
In a previous paper we lifted Charles Rezk’s complete Segal model structure on the category of simplicial spaces to a Quillen equivalent one on the category of “relative categories” and our aim in thi...
The groupoidal analogue Theta~ to Joyal's category Theta is a test category
1-category 1-groupoid cellular category décalage
2011/2/23
We introduce the groupoidal analogue e to Joyal’s cellular category and we prove that e is a strict test category in the sense of Grothendieck.