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...

We describe a symplectization functor from the Poisson category to the symplectic “category” and we study some of its properties.

The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this transformation is a left exact functor. This functor and its first derived functor are evaluated on the global sections of a line bundle on the flag variety...

The preservation of weak pullbacks is studied for a functor M 1 on the category UMS of ultrametric spaces and nonexpansive mappings. The functor M 1 associates with an ultrametric space its collection of Borel probability measures with compact support. By application of the Max-ow Min-cut Theorem of graph theory a mediating morphism for a weak pullback diagram can be constructed in SET. It is s...

Consider a coring with exact rational functor, and a finitely generated and projective right comodule. We construct a functor (coinduction functor) which is right adjoint to the hom-functor represented by this comodule. Using the coinduction functor, we establish a bijective map between the set of representative classes of torsion simple right comodules and the set of representative classes of ...