Rigidification of connective comodules

We show that we can rigidify homotopy coherent comodules in connective modules over the Eilenberg-Mac Lane spectrum of a field, or more generally of a finite product of fields $\mathbb{k}$. That is, the $\infty$-category of homotopy coherent comodules is represented by a model category of strict comodules in non-negative chain complexes over $\mathbb{k}$ or in simplicial $\mathbb{k}$-modules. These comodules are over a coalgebra that is strict and simply connected. The rigidification result allows us to derive the notion of cotensor product of comodules and endows the $\infty$-category of comodules with a symmetric monoidal structure. We lift the usual Dold-Kan correspondance to these model categories of comodules. We also show a rigidification result for comodules in the non-connective case when the coalgebra is dualizable. To prove these results, we introduce Postnikov towers of comodules that dualize the cellularity of combinatorial model categories. Moreover, we define the notion of symmetric comonoidal Quillen model categories and weak comonoidal Quillen equivalences in order to describe the homotopical behavior of our derived cotensor product of comodules.Comment: 60 page

Classical and MgII-selected Damped Lyman-alpha Absorbers: impact on Omega_HI at z<1.7

The Damped Lyman-alpha systems (DLAs), seen in absorption in the spectrum of quasars, are believed to contain a large fraction of the neutral gas in the Universe. Paradoxically, these systems are more difficult to observe at z_abs<1.7, since they are rare and their HI feature then falls in UV spectra. Rao & Turnshek (2000) pioneered a method based on MgII-selected DLAs, that is absorbers discovered thanks to our knowledge of their MgII feature in optical spectra. We use new observations undertaken at the TNG as well as a careful literature & archival search to build samples of low redshift absorbers classified according to the technique used for their discovery. We successfully recover N(HI) and equivalent widths of FeII 2600, MgII 2796, MgII 2803 and MgII 2852 for a sample of 36 absorbers, 21 of which are MgII-selected. We find that the MgII-selected sample contains a marginally larger fraction of absorbers with log N(HI)>21.0 than seen otherwise at low redshift. If confirmed, this property will in turn affect estimates of Omega_HI which is dominated by the highest HI column densities. We find that log N(HI) does not correlate significantly with metal equivalent widths. Similarly, we find no evidence that gravitational lensing, the fraction of associated systems or redshift evolution affect the absorber samples in a different way. We conclude that the hint of discrepancies in N(HI) distributions most likely arises from small number statistics. Therefore, further observations are required to better clarify the impact of this discrepancy on estimates of Omega_HI at low redshift.Comment: 13 pages, 8 figures. Accepted for publication in MNRA

Revisiting the origin of the high metallicities of sub-damped Lyman-alpha systems

Sub-damped Lyman-alpha systems (sub-DLAs) have previously been found to exhibit a steeper metallicity evolution than the classical damped Lyman-alpha systems (DLAs), evolving to close to solar metallicity by z~1. From new high-resolution spectra of 17 sub-DLAs we have increased the number of measurements of [Fe/H] at z<1.7 by 25% and compiled the most complete literature sample of sub-DLA and DLA abundances to date. We find that sub-DLAs are indeed significantly more metal-rich than DLAs, but only at z<1.7; the metallicity distributions of sub-DLAs and DLAs at z>1.7 are statistically consistent. We also present the first evidence that sub-DLAs follow a velocity width-metallicity correlation over the same velocity range as DLAs, but the relation is offset to higher metallicities than the DLA relation. On the basis of these results, we revisit the previous explanation that the systematically higher metallicities observed in sub-DLAs are indicative of higher host galaxy masses. We discuss the various problems that this interpretation encounters and conclude that in general sub-DLAs are not uniquely synonymous with massive galaxies. We rule out physically related sources of bias (dust, environment, ionization effects) and examine systematics associated with the selection and analysis of low-redshift sub-DLAs. We propose that the high metallicities of sub-DLAs at z<1.7 that drives an apparently steep evolution may be due to the selection of most low-redshift sub-DLAs based on their high MgII equivalent widths.Comment: 6 pages, 3 figures, MNRAS, in pres

Parsec-scale HI absorption structure in a low-redshift galaxy seen against a Compact Symmetric Object

We present global VLBI observations of the 21-cm transition of atomic hydrogen seen in absorption against the radio source J0855+5751. The foreground absorber (SDSS~J085519.05+575140.7) is a dwarf galaxy at $z$ = 0.026. As the background source is heavily resolved by VLBI, the data allow us to map the properties of the foreground HI gas with a spatial resolution of 2pc. The absorbing gas corresponds to a single coherent structure with an extent $>$35pc, but we also detect significant and coherent variations, including a change in the HI optical depth by a factor of five across a distance of $\leq$6pc. The large size of the structure provides support for the Heiles & Troland model of the ISM, as well as its applicability to external galaxies. The large variations in HI optical depth also suggest that caution should be applied when interpreting $T_S$ measurements from radio-detected DLAs. In addition, the distorted appearance of the background radio source is indicative of a strong jet-cloud interaction in its host galaxy. We have measured its redshift ($z$ = 0.54186) using optical spectroscopy on the William Herschel Telescope and this confirms that J0855+5751 is a FRII radio source with a physical extent of $<$1kpc and supports the previous identification of this source as a Compact Symmetric Object. These sources often show absorption associated with the host galaxy and we suggest that both HI and OH should be searched for in J0855+5751.Comment: 14 pages and 10 figures. Accepted for publication in MNRA

Statistical Properties of DLAs and sub-DLAs

Quasar absorbers provide a powerful observational tool with which to probe both galaxies and the intergalactic medium up to high redshift. We present a study of the evolution of the column density distribution, f(N,z), and total neutral hydrogen mass in high-column density quasar absorbers using data from a recent high-redshift survey for damped Lyman-alpha (DLA) and Lyman limit system (LLS) absorbers. Whilst in the redshift range 2 to 3.5, ~90% of the neutral HI mass is in DLAs, we find that at z>3.5 this fraction drops to only 55% and that the remaining 'missing' mass fraction of the neutral gas lies in sub-DLAs with N(HI) 10^{19} - 2 * 10^{20} cm^{-2}.Comment: 6 pages, 4 figures, in "Chemical Enrichment of Intracluster and Intergalactic medium", Proceedings of the Vulcano Workshop, May 14-18, 200

Coinductive control of inductive data types

We combine the theory of inductive data types with the theory of universal measurings. By doing so, we find that many categories of algebras of endofunctors are actually enriched in the corresponding category of coalgebras of the same endofunctor. The enrichment captures all possible partial algebra homomorphisms, defined by measuring coalgebras. Thus this enriched category carries more information than the usual category of algebras which captures only total algebra homomorphisms. We specify new algebras besides the initial one using a generalization of the notion of initial algebra.Comment: 21 page