The homotopy theory of coalgebras over a comonad

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We provide concrete examples that satisfy our conditions and are relevant in descent theory and in the theory of Hopf-Galois extensions. These examples are specific instances of the following categories of comodules over a coring. For any semihereditary commutative ring R, let A be a dg R-algebra that is homologically simply connected. Let V be an A-coring that is semifree as a left A-module on a degreewise R-free, homologically simply connected graded module of finite type. We show that there is a model category structure on the category of right A-modules satisfying the conditions of our existence theorem with respect to the comonad given by tensoring over A with V and conclude that the category of V-comodules in the category of right A-modules admits a model category structure of the desired type. Finally, under extra conditions on R, A, and V, we describe fibrant replacements in this category of comodules in terms of a generalized cobar construction.Comment: 34 pages, minor corrections. To appear in the Proceedings of the London Mathematical Societ

Waldhausen K-theory of spaces via comodules

Let $X$ be a simplicial set. We construct a novel adjunction between the categories of retractive spaces over $X$ and of $X_{+}$-comodules, then apply recent work on left-induced model category structures (arXiv:1401.3651v2 [math.AT],arXiv:1509.08154 [math.AT]) to establish the existence of a left proper, simplicial model category structure on the category of $X_+$-comodules, with respect to which the adjunction is a Quillen equivalence after localization with respect to some generalized homology theory. We show moreover that this model category structure stabilizes, giving rise to a model category structure on the category of $\Sigma^\infty X_{+}$-comodule spectra. The Waldhausen $K$-theory of $X$, $A(X)$, is thus naturally weakly equivalent to the Waldhausen $K$-theory of the category of homotopically finite $\Sigma^\infty X_{+}$-comodule spectra, with weak equivalences given by twisted homology. For $X$ simply connected, we exhibit explicit, natural weak equivalences between the $K$-theory of this category and that of the category of homotopically finite $\Sigma^{\infty}(\Omega X)_+$-modules, a more familiar model for $A(X)$. For $X$ not necessarily simply connected, we have localized versions of these results. For $H$ a simplicial monoid, the category of $\Sigma^{\infty}H_{+}$-comodule algebras admits an induced model structure, providing a setting for defining homotopy coinvariants of the coaction of $\Sigma^{\infty}H_{+}$ on a $\Sigma^{\infty}H_{+}$-comodule algebra, which is essential for homotopic Hopf-Galois extensions of ring spectra as originally defined by Rognes in arXiv:math/0502183v2} and generalized in arXiv:0902.3393v2 [math.AT]. An algebraic analogue of this was only recently developed, and then only over a field (arXiv:1401.3651v2 [math.AT]).Comment: 48 pages, v3: some technical modifications, to appear in Advances in Mathematic

A necessary and sufficient condition for induced model structures

A common technique for producing a new model category structure is to lift the fibrations and weak equivalences of an existing model structure along a right adjoint. Formally dual but technically much harder is to lift the cofibrations and weak equivalences along a left adjoint. For either technique to define a valid model category, there is a well-known necessary "acyclicity" condition. We show that for a broad class of "accessible model structures" - a generalization introduced here of the well-known combinatorial model structures - this necessary condition is also sufficient in both the right-induced and left-induced contexts, and the resulting model category is again accessible. We develop new and old techniques for proving the acyclity condition and apply these observations to construct several new model structures, in particular on categories of differential graded bialgebras, of differential graded comodule algebras, and of comodules over corings in both the differential graded and the spectral setting. We observe moreover that (generalized) Reedy model category structures can also be understood as model categories of "bialgebras" in the sense considered here.Comment: 49 pages; final journal version to appear in the Journal of Topolog

Survival and Nesting Habitat use by Sichuan and Ring-necked Pheasants Released in Ohio

Author Institution: Ohio Dept of Natural Resources, Division of Wildlife, Olentangy Wildlife Research Station, Ashley, OHRing-necked pheasant (Phasianus colchicus) populations in the Midwestern United States have declined drastically since World War II. Population numbers in Ohio have leveled off since the establishment of the Conservation Reserve Program (CRP); however, a return to historically abundant ring-necked pheasant populations is unlikely with current land-use practices. Studies by the Michigan Department of Natural Resources (DNR) of released Sichuan pheasants (P. c. strauchi), a subspecies of the ring-necked pheasant, suggested that Sichuans may nest in woody cover, a trait that could reduce agriculture-related nest losses common to ring-necked pheasants and potentially increase pheasant populations. We released over 2,000 Sichuan pheasants (962 females, 1,116 males) and 208 ring-necked pheasants (24 females, 84 males) in central Ohio, United States, in early April 1993-96. Survival and habitat use before, during, and after the nesting season were evaluated for a sample of hens from each subspecies through the use of radio-telemetry. Survival rates (range = 0.05-0.15) and apparent nest success (38% and 50% for Sichuan and ring-necked nests, respectively) were not different between the subspecies. The largest source of mortality for both subspecies was predation (71-84% and 65-88%, for Sichuan and ring-necked hens, respectively). Most nests, 85% of Sichuan and 81% of ring-necked, were located in upland herbaceous, upland shrub/scrub, and hay macro-habitat types. Nests of both subspecies were within 16 m of an edge, surrounded by few woody stems (median = 0.25/m2) and dense herbaceous cover (1,450 and 1,130 stems/m2, Sichuan and ring-necked nests, respectively). Sichuan hens selected a higher proportion of forbs (37.5% and 15.0%, Sichuan and ring-necked, respectively) and ring-necked hens selected a higher proportion of grass (17.5% and 37.5%, Sichuan and ring-necked, respectively) within 1.0 m2 of the nest (P ≤ 0.010). Population survey indices suggested that a self-sustaining Sichuan pheasant population was not established

Left-induced model structures and diagram categories

We prove existence results a la Jeff Smith for left-induced model category structures, of which the injective model structure on a diagram category is an important example. We further develop the notions of fibrant generation and Postnikov presentation from Hess, which are dual to a weak form of cofibrant generation and cellular presentation. As examples, for k a field and H a differential graded Hopf algebra over k, we produce a left-induced model structure on augmented H-comodule algebras and show that the category of bounded below chain complexes of finite-dimensional k-vector spaces has a Postnikov presentation. To conclude, we investigate the fibrant generation of (generalized) Reedy categories. In passing, we also consider cofibrant generation, cellular presentation, and the small object argument for Reedy diagrams.Comment: 33 pages; v2 fixes an error in the construction of the Postnikov presentation in section 3 and contains several minor improvements suggested by the referee. To appear in the Proceedings of the August 2013 "Women in Topology" workshop at BIRS, which will be published by Contemporary Mathematic

Strategies for effective unmanned aerial vehicle use in geological field studies based on cognitive science principles

Field geologists are increasingly using unmanned aerial vehicles (UAVs or drones), although their use involves significant cognitive challenges for which geologists are not well trained. On the basis of surveying the user community and documenting experts’ use in the field, we identified five major problems, most of which are aligned with well-documented limits on cognitive performance. First, the images being sent from the UAV portray the landscape from multiple different view directions. Second, even with a constant view direction, the ability to move the UAV or zoom the camera lens results in rapid changes in visual scale. Third, the images from the UAVs are displayed too quickly for users, even experts, to assimilate efficiently. Fourth, it is relatively easy to get lost when flying, particularly if the user is unfamiliar with the area or with UAV use. Fifth, physical limitations on flight time are a source of stress, which renders the operator less effective. Many of the strategies currently employed by field geologists, such as postprocessing and photogrammetry, can reduce these problems. We summarize the cognitive science basis for these issues and provide some new strategies that are designed to overcome these limitations and promote more effective UAV use in the field. The goal is to make UAV-based geological interpretations in the field possible by recognizing and reducing cognitive loa

Learning from the COVID-19 Pandemic: How Faculty Experiences Can Prepare Us for Future System-Wide Disruption

The COVID-19 pandemic provided education researchers with a natural experiment: an opportunity to investigate the impacts of a system-wide, involuntary move to online teaching and to assess the characteristics of individuals who adapted more readily. To capture the impacts in real time, our team recruited college-level geoscience instructors through the National Association of Geoscience Teachers (NAGT) and American Geophysical Union (AGU) communities to participate in our study in the spring of 2020. Each weekday for three successive weeks, participants (n = 262) were asked to rate their experienced disruption in four domains: teaching, research, ability to communicate with their professional community, and work-life balance. The rating system (a scale of 1–5, with 5 as severely disrupted) was designed to assess (a) where support needs were greatest, (b) how those needs evolved over time, and (c) respondents’ capacity to adapt. In addition, participants were asked two open-response questions, designed to provide preliminary insights into how individuals were adapting—what was their most important task that day and what was their greatest insight from the previous day. Participants also provided information on their institution type, position, discipline, gender, race, dependents, and online teaching experience (see supplemental material)

Never underestimate SES workers: volunteers - a case in point

While the main emphasis of the chapter is on the ways that emergency services (ES) volunteers cope, it also explores the concept that ER protocols, or the lack thereof, may reinforce resilience, or during critical incidents add sufficient strain to produce burnout among ES volunteers. While the overall findings of our reaearch reveal an ongoing and amazing resilience in ES volunteers, it will be postulated that where there are no organizational protocols to provide the rules for all types of rescue situations and outcomes, the level of stress on some volunteers can be very great. Qualitative accounts from volunteers give us an insight into why they volunteer, what they gain from working in the emergency services area and tips on how to stay sane under stressful conditions