Speaker: Gregory Arone (Virginia) Title: Part 1: operads, modules and the chain rule Abstract: Let F be a homotopy functor between the categories of pointed topological spaces or spectra. By the work of Goodwillie, the derivatives of F form a symmetric sequence of spectra ∂∗F . This symmetric sequence determines the homogeneous layers in the Taylor tower of F , but not the extensions in the tow...

" First quantization is a mystery, but second quantization is a func-tor " (E. Nelson) Comme l'on sait la " quantification geometrique " consiste a rechercher un certain foncteur de la categorie des varietes symplectiques et sym-plectomorphismes dans celle des espaces de Hilbert complexes et des transformations unitaires (.. .) Il est bien connu qu'un tel foncteur n'existe pas. Abstract We defi...

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

Let k be a field of characteristic p. We construct a new inflation functor for cohomological Mackey functors for finite groups over k. Using this inflation functor, we give an explicit presentation of the graded algebra of self extensions of the simple functor S 1 , when p is odd and G is an elementary abelian p-group. AMS Subject Classification : 18A25, 18G10, 18G15, 20J05.

We study the functor `2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and both categories are enriched over algebraic domains. The functor preserves daggers, monoidal structures, enrichment, and various (co)limits, but has no adjoints. Up to unitaries, its direct image consists precisely of the partial isometries, but its ...

Since the inception of the notion of fuzzy topology much attention was paid to the possible means of interaction between fuzzy and crisp topological settings, in order to see whether fuzzy topology was doing anything new. In particular, different functors relating the categories Top of topological spaces and L-Top of Ltopological spaces (L being a suitable complete lattice) appeared in the lite...

We study a connection between mapping spaces of bimodules and infinitesimal over an operad. As main application motivation our work, we produce explicit delooping the manifold calculus tower associated to space smooth maps D m → n $D^m\rightarrow D^n$ discs, ⩾ $n\geqslant m$ , avoiding any given multisingularity coinciding with standard inclusion near boundary ∂ $\partial D^m$ . In particular, ...