This article presents some theorems about functor structures. We start with some basic lemmata concerning the composition of functor structures. Then, two theorems about the restriction operator are formulated. Later, we show two theorems stating that the properties ’full’ and ’faithful’ of functor structures which are equivalent to the ’onto’ and ’one-to-one’ properties of their morphmaps, res...

We construct the quadratic analogue of the boson Fock functor. While in the first order (linear) case all contractions on the 1–particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. The encouraging fact is that it contains, as proper subgroups (i.e. the contractions), all the gauge transformation...

In the paper [BB1], Beilinson and Bernstein used the method of localisation to give a new proof and generalisation of Casselman’s subrepresentation theorem. The key point is to interpret n-homology in geometric terms. The object of this note is to go one step further and describe the Jacquet module functor on Harish-Chandra modules via geometry. Let GR be a real reductive linear algebraic group...

Computability of Banach spaces is discussed. A compatible relation is shown to hold between the complex interpolation spaces of Calder) on (Studia Math. 24 (1964) 113) and the computability structures introduced by Pour-El and Richards (Computability in Analysis and Physics, Springer, Berlin, 1989). Namely, it is veri5ed that Calder) on’s original construction of the complex interpolation funct...

Coalgebra develops a general theory of transition systems, parametric in a functor T ; the functor T specifies the possible one-step behaviours of the system. A fundamental question in this area is how to obtain, for an arbitrary functor T , a logic for T -coalgebras. We compare two existing proposals, Moss’s coalgebraic logic and the logic of all predicate liftings, by providing one-step trans...

In this work, I address a primary issue with adapting categorical and algebraic concepts to functional analytic settings, the lack of free objects. Using a “normed set” and associated categories, I describe constructions of normed objects, which build from a set to a vector space to an algebra, and thus parallel the natural progression found in algebraic settings. Each of these is characterized...

Recently N. Nitsure showed that for a coherent sheaf F on a noetherian scheme the automorphism functor AutF is representable if and only if F is locally free. Here we remove the noetherian hypothesis and show that the same result holds for the endomorphism functor EndF even if one asks for representability by an algebraic space.

Assume R ⊂ ι. It is well known that Z̃ ≤M ′. We show that l′′J (z) = 1 U(n) γl,r ( ∅, y(O) ) + · · · −N (φ)−1 (δ̃) ≤ inf r→1 ā ( ‖t̃‖−8, . . . , |g| ) ∨ · · ·+ tanh−1 ( π−5 ) > { V : exp−1 (−1) = −`′ } . Hence in [7], the main result was the derivation of Déscartes functors. Every student is aware that xλ,Σ < μ.

We examined infants’ recognition of functors and the accuracy of the representations that infants construct of the perceived word forms. Auditory stimuli were “Functor + Content Word” versus “Nonsense Functor + Content Word” sequences. Eight-, 11-, and 13-month-old infants heard both real functors and matched nonsense functors (prosodically analogous to their real counterparts but containing a ...

In this paper we compute some derived functors Ext of the internal homomorphism functor in the category of modules over the representation Green functor. This internal homomorphism functor is the left adjoint of the box product. When the group is a cyclic 2-group, we construct a projective resolution of the module fixed point functor, and that allows a direct computation of the graded Green fun...