Locally class-presentable and class-accessible categories

We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. This generalization is intended for applications in the abstract homotopy theory

The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is the study of the homotopy theory of dg-categories up to quasi-equivalences. Our main result provides a natural description of the mapping spaces between two dg-categories $C$ and $D$ in terms of the nerve of a certain category of $(C,D)$-bimodules. We also prove that the homotopy category $Ho(dg-Cat)$ is cartesian closed (i.e. possesses internal Hom's relative to the tensor product). We use these two results in order to prove a derived version of Morita theory, describing the morphisms between dg-categories of modules over two dg-categories $C$ and $D$ as the dg-category of $(C,D)$-bi-modules. Finally, we give three applications of our results. The first one expresses Hochschild cohomology as endomorphisms of the identity functor, as well as higher homotopy groups of the \emph{classifying space of dg-categories} (i.e. the nerve of the category of dg-categories and quasi-equivalences between them). The second application is the existence of a good theory of localization for dg-categories, defined in terms of a natural universal property. Our last application states that the dg-category of (continuous) morphisms between the dg-categories of quasi-coherent (resp. perfect) complexes on two schemes (resp. smooth and proper schemes) is quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect) on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm. 8.15 is new. Minor corrections. Final version, to appear in Inventione

Beam asymmetry Sigma for pi(+) and pi(0) photoproduction on the proton for photon energies from 1.102 to 1.862 GeV

Beam asymmetries for the reactions gamma p -\u3e p pi(0) and gamma p -\u3e n pi(+) have been measured with the CEBAF Large Acceptance Spectrometer (CLAS) and a tagged, linearly polarized photon beam with energies from 1.102-1.862 GeV. A Fourier moment technique for extracting beam asymmetries from experimental data is described. The results reported here possess greater precision and finer energy resolution than previous measurements. Our data for both pion reactions appear to favor the SAID and Bonn-Gatchina scattering analyses over the older Mainz MAID predictions. After incorporating the present set of beam asymmetries into the world database, exploratory fits made with the SAID analysis indicate that the largest changes from previous fits are for properties of the Delta(1700)3/2(-) and Delta(1905) 5/2(+) states

N∗→Nη′N^*\to N \eta^\prime decays from photoproduction of η′\eta^\prime-mesons off protons

A study of the partial-wave content of the $\gamma p\to \eta^\prime p$ reaction in the fourth resonance region is presented, which has been prompted by new measurements of polarization observables for that process. Using the Bonn-Gatchina partial-wave formalism, the incorporation of new data indicates that the $N(1895)1/2^-$, $N(1900)3/2^+$, $N(2100)1/2^+$, and $N(2120)3/2^-$ are the most significant contributors to the photoproduction process. New results for the branching ratios of the decays of these more prominent resonances to $N\eta^\prime$ final states are provided; such branches have not been indicated in the most recent edition of the Review of Particle Properties. Based on the analysis performed here, predictions for the helicity asymmetry $E$ for the $\gamma p\to \eta^\prime p$ reaction are presented.Comment: 7 pages, 5 figures, 3 table

A colimit decomposition for homotopy algebras in Cat

Badzioch showed that in the category of simplicial sets each homotopy algebra of a Lawvere theory is weakly equivalent to a strict algebra. In seeking to extend this result to other contexts Rosicky observed a key point to be that each homotopy colimit in simplicial sets admits a decomposition into a homotopy sifted colimit of finite coproducts, and asked the author whether a similar decomposition holds in the 2-category of categories Cat. Our purpose in the present paper is to show that this is the case.Comment: Some notation changed; small amount of exposition added in intr

Chiral constituent quark model study of the process γp→ηp\gamma p \to \eta p

A constituent quark model is developed for the reaction, allowing us to investigate all available data for differential cross sections as well as single polarization asymmetries (beam and target) by including {\it all} of the PDG, one to four star, nucleon resonances ($S_{11}$, $P_{11}$, $P_{13}$, $D_{13}$, $D_{15}$, $F_{15}$, $F_{17}$, $G_{17}$, $G_{19}$, $H_{19}$, $I_{1,11}$, and $K_{1,13}$). Issues related to the missing resonances are also briefly discussed by examining possible contributions from several new resonances ($S_{11}$, $P_{11}$, $P_{13}$, $D_{13}$, $D_{15}$, and $H_{1,11}$).Comment: 3 pages,2 figures, presented in NSTAR2007, Bonn, Germany,5 - 8 September 200

Towers and fibered products of model categories

Given a left Quillen presheaf of localized model structures, we study the homotopy limit model structure on the associated category of sections. We focus specifically on towers and fibered products of model categories. As applications we consider Postnikov towers of model categories, chromatic towers of spectra and Bousfield arithmetic squares of spectra. For spectral model categories, we show that the homotopy fiber of a stable left Bousfield localization is a stable right Bousfield localization