相关论文: Symmetric Self-Adjunctions and Matrices

We construct a structure of a ring with local units on a co-Frobenius coalgebra. We study a special class of co-Frobenius coalgebras whose objects we call symmetric coalgebras. We prove that any semiperfect coalgebra can be embedded in a…

We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…

Let $\mathcal{C}$ be a finite braided multitensor category. Let $B$ be Majid's automorphism braided group of $\mathcal{C}$, then $B$ is a cocommutative Hopf algebra in $\mathcal{C}$. We show that the center of $\mathcal{C}$ is isomorphic to…

Voevodsky's derived category of motives is the main arena today for the study of algebraic cycles and motivic cohomology. In this paper we study whether the inclusions of three important subcategories of motives have a left or right…

Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality.…

It is known that the so-called monadic decomposition, applied to the adjunction connecting the category of bialgebras to the category of vector spaces via the tensor and the primitive functors, returns the usual adjunction between…

Two adjoint functors can be seen as generalisations of the two functions within a Galois connection. If instead the adjoints are not generalised from functions, but from relations, then analogously the object of study becomes a more general…

It is known that factorisation systems in categories can be viewed as unitary pseudo algebras for the "squaring" monad in Cat. We show in this note that an analogous fact holds for proper (i.e., epi-mono) factorisation systems and a…

In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves…

Grothendieck proved that if $f:X\longrightarrow Y$ is a proper morphism of nice schemes, then $Rf_*$ has a right adjoint, which is given as tensor product with the relative canonical bundle. The original proof was by patching local data.…

Every transformation monoid comes equipped with a canonical topology-the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This…

We show that any adjoint absolutely simple linear algebraic group over a field of characteristic zero is the automorphism group of some projector on a central simple algebra. Projective homogeneous varieties can be described in these terms;…

The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theories with matter is analysed as an isomonodromy problem. We show that the holomorphic section describing the effective action can be deformed by moving its singularities on…

We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian groups. As a consequence, every object in…

This paper lays the groundwork for the theory of categorical diagonalization. Given a diagonalizable operator, tools in linear algebra (such as Lagrange interpolation) allow one to construct a collection of idempotents which project to each…

A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…

We prove that the trace of the Frobenius endofunctor of the category of automorphic sheaves with nilpotent singular support maps isomorphically to the space of unramified automorphic functions, settling a conjecture from [AGKRRV1]. More…

We consider an oriented version of the stable symplectic category defined in \cite{N}. We show that the group of monoidal automorphisms of this category, that fix each object, contains a natural subgroup isomorphic to the solvable quotient…

We study finitary 2-categories associated to dual projection functors for finite dimensional associative algebras. In the case of path algebras of admissible tree quivers (which includes all Dynkin quivers of type A) we show that the monoid…

Given a monad and a comonad, one obtains a distributive law between them from lifts of one through an adjunction for the other. In particular, this yields for any bialgebroid the Yetter-Drinfel'd distributive law between the comonad given…