Related papers: When is Existential Quantification Conservative?
There exists a canonical functor from the category of fibrant objects of a model category modulo cylinder homotopy to its homotopy category. We show that this functor is faithful under certain conditions, but not in general.
Given an action of an affine algebraic group with only trivial characters on a factorial variety, we ask for categorical quotients. We characterize existence in the category of algebraic varieties. Moreover, allowing constructible sets as…
It is shown here how the semiclassical theory of electrical susceptibility can be extended to the case in which both radiation and matter are quantized. This is done specifically for the cases of linear and second order susceptibilities.…
Preserving entanglement is a crucial dynamical process for entanglement-based quantum computation and quantum-information processes, such as one-way quantum computing and quantum key distribution. However, the problem of quantifying the…
We give necessary and sufficient conditions for non-conservativity of a class of minimal quantum dynamical semigroups (qds). We extend some well known criteria for conservativity of minimal qds and show interesting relations of the…
We study abelian quotient categories A=T/J, where T is a triangulated category and J is an ideal of T. Under the assumption that the quotient functor is cohomological we show that it is representable and give an explicit description of the…
For any algebra morphism in a monoidal category, we provide sufficient conditions (which are also necessary if the unit is a left tensor generator) for the attached induction functor being semiseparable. Under mild assumptions, we prove…
We give necessary and sufficient conditions to have measurable and continuous eigenfunctions for linearly recurrent Cantor dynamical systems. We also construct explicitly an example of linearly recurrent system with nontrivial Kronecker…
In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G=GL_2$ over a definite quaternion algebra $D/\Q$. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having…
We investigate fundamental properties of adjoint functors to the precomposition functor in the category of strict polynomial functors.
Given a dissipative operator $A$ on a complex Hilbert space $\mathcal{H}$ such that the quadratic form $f\mapsto \mbox{Im}\langle f,Af\rangle$ is closable, we give a necessary and sufficient condition for an extension of $A$ to still be…
The Fourier transform is considered as a Henstock--Kurzweil integral. Sufficient conditions are given for the existence of the Fourier transform and necessary and sufficient conditions are given for it to be continuous. The…
We provide a characterization of finite \'etale morphisms in tensor triangular geometry. They are precisely those functors which have a conservative right adjoint, satisfy Grothendieck--Neeman duality, and for which the relative dualizing…
We define a functor which takes in an $(\infty,1)$-category and outputs an $(\omega,1)$-category, the natural maximally "strict" version of an $(\infty,1)$-category. We do this by modeling $(\infty,1)$-categories as categories enriched in…
We consider the forced harmonic oscillator quantized according to infinite statistics ( a special case of the `quon' algebra proposed by Greenberg ). We show that in order for the statistics to be consistently evolved the forcing term must…
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation…
In this article we extend evaluations of the Kauffman bracket on regular isotopy classes of knots and links to a variety of functors defined on the category of framed tangles. We show that many such functors exist, and that they correspond…
We extend Lurie's definition of enriched $\infty$-categories to notions of left enriched, right enriched and bienriched $\infty$-categories, which generalize the concepts of closed left tensored, right tensored and bitensored…
Given a 0-connective motivic spectrum $E \in SH(k)$ over a perfect field k, we determine $h_0$ of the associated motive $M E \in DM(k)$ in terms of $\pi_0 (E)$. Using this we show that if k has finite 2-\'etale cohomological dimension, then…
In many Lagrangian field theories one has a Poisson bracket defined on the space of local functionals. We find necessary and sufficient conditions for a transformation on the space of local functionals to be canonical in three different…