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 ...

We give a new construction for the n-th Taylor polynomial, in the sense of Goodwillie calculus, for homotopy functors from spectra to spectra. We then use this model to classify n-excisive functors of module categories of functors with smash product (FSPs) by bi-modules of explicit FSPs. Introduction: In [Cal3], T. Goodwillie constructs a Taylor tower for functors from spectra to spectra. The l...

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...

The main result of [Barr (1967)] is that the cohomology of an algebra with respect to the free associate algebra cotriple can be described by the resolution given by U. Shukla in [Shukla (1961)]. That looks like a composite resolution; first an algebra is resolved by means of free modules (over the ground ring) and then this resolution is given the structure of a DG-algebra and resolved by the ...

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

Let C, C be curves over a base scheme S with g(C) ≥ 2. Then the functor T 7→ {generically smooth T -morphisms T ×S C ′ → T ×S C} from ((Sschemes)) to ((sets)) is represented by a quasi-finite unramified S-scheme. From this one can deduce that for any two integers g ≥ 2 and g, there is an integer M(g, g) such that for any two curves C,C over any field k with g(C) = g, g(C) = g, there are at most...

Given an arbitrary locally finitely presentable category K and finitary monads T and S on K , we characterize monad morphisms α : S −→ T with the property that the induced functor α∗ : K T −→ K S between the categories of Eilenberg-Moore algebras is fully faithful. We call such monad morphisms dense and give a characterization of them in the spirit of Beth’s definability theorem: α is a dense m...

This note explains consequences of recent work of Frank Quinn for computations of Nil groups in algebraic K-theory, in particular the Nil groups occurring in the K-theory of polynomial rings, Laurent polynomial rings, and the group ring of the infinite dihedral group. 1. Statement of Results Let R be a ring with unit. For an integer q, let KqR be the algebraic K-group of Bass and Quillen. Bass ...

If C is an abelian category, the category Ind(C) of ind-objects of C has many remarkable properties: it is much bigger than C, it contains C, and furthermore it is dual (in a certain sense) to C. We introduce here the category of ind-sheaves on a locally compact space X as the category of ind-objects of the category of sheaves with compact supports. This construction has some analogy with that ...