Enriched Kleisli Objects for Pseudomonads

In the enriched setting, the notions of injective and projective model structures on a category of enriched diagrams also make sense. In this paper, we prove the existence of these model structures on enriched diagram categories under local presentability, accessibility, and "acyclicity" conditions, using the methods of lifting model structures from an adjunction introduced by Garner, Hess, Kedziorek, Riehl, and Shipley.

In this note we prove that Reedy fibrant Segal categories are fibrant objects in the model category structure S C c \mathcal {SC}_c . Combining this result with a previous one, we thus have that the fibrant objects are precisely the Reedy fibrant Segal categories. We also show that the analogous result holds for Segal categories that are fibrant in the projective model structure on simplicial spaces, considered as objects in the model structure S C f \mathcal {SC}_f .

We first study commutative, pointed monoids providing basic definitions and results in a manner similar commutative ring theory. Included are results on chain conditions, primary decomposition as well as normalization for a special class of monoids which lead to a study monoid schemes, divisors, Picard groups and class groups. It is shown that the normalization of a monoid need not be a monoid, but possibly a monoid scheme. After giving the definition of, and basic results for, $A$-sets, we classify projective $A$-sets and show they are completely determine by their rank. Subsequently, for a monoid $A$, we compute $K_0$ and $K_1$ and prove the Devissage Theorem for $G_0$. With the definition of short exact sequence for $A$-sets in hand, we describe the set $Ext(X,Y)$ of extensions for $A$-sets $X,Y$ and classify the set of square-zero extensions of a monoid $A$ by an $A$-set $X$ using the Hochschild cosimplicial set. We also examine the projective model structure on simplicial $A$-sets showcasing the difficulties involved in computing homotopy groups as well as determining the derived category for a monoid. The author defines the category $\operatorname{Da}(\mathcal{C})$ of double-arrow complexes for a class of non-abelian categories $\mathcal{C}$ and, in the case of $A$-sets, shows an adjunction with the category of simplicial $A$-sets.

In this note we study the local projective model structure on presheaves of complexes on a site, that is, we describe its classes of cofibrations, fibrations, and weak equivalences. In particular, we prove that the fibrant objects are those satisfying descent with respect to all hypercovers. We also describe cofibrant and fibrant replacement functors with pleasant properties.

Nonrigid Structure-From-Motion is a well-known approach to estimate time-varying 3D structures from 2D input image sequences. For challenging problems such as the reconstruction of human faces, state-of-the-art approaches estimate statistical shape spaces from training data. It is common practice to use orthographic or weak-perspective camera models to map 3D to 2D points. We propose to use a projective camera model combined with a multilinear tensor-based face model, enabling approximation of a dense 3D face surface by sparse 2D landmarks. Using a projective camera is beneficial, as it is able to handle perspective projections and particular camera motions which are critical for affine models. We show how the nonlinearity of the projective model can be linearized so that its parameters can be estimated by an alternating-least-squares approach. This enables simple and fast estimation of the model parameters. The effectiveness of the proposed algorithm is demonstrated using challenging real image data.

Structure is one of the most important properties of man-made objects, and it is beneficial for a number of applications. In this paper, we propose an effective method to recognize the 3-D building models’ compositional structures, which represent the basic knowledge of human beings on the shape formation of the models in 3-D space. To overcome the shortcomings of the traditional algorithms that are focused on the detailed geometric features of the surface meshes, volumetric analysis is employed here to study the compositional structures of the building models from inside. To describe the general shape of a building model in 3-D space, the model is voxelized, and layered distance maps are generated to record its volumetric characteristics at different places. With reference to the value variation of the layered distance maps in the horizontal and vertical directions, different structural parts are identified in the voxel space, and the valid voxels are classified accordingly to obtain the voxel representation of each part. Based on the volume decomposition result, an extended topological graph is then constructed for description of the compositional structure of the building model. As the spatial relationships between different parts are analyzed from inside and the whole process is implemented in the voxel space, the method is immune to the complicated and confusing features on the surfaces of the building models, with the scale of the structure recognition determined by the discretizing resolution of the voxel space. In the experiments, three typical building models are chosen for discussion of the effectiveness and efficiency of the proposed approach, and some example applications are shown to demonstrate its potential usage in different fields.

This thesis, which presents a new approach to the algebraic K-theory, is divided into two parts. The first one is devoted to the category of small simplicial categories. First, we construct a new model structure on sCat = [Δop,Cat] which is called the diagonal model structure, in reference to the diagonal model structure of Moerdijk on bisimplicial sets sSet2. Then we show that the new structure is proper and cellular. Note that this new model structure is not tensored and cotensored over the category of simplicial sets sSet in a manner consistent with the model structure. To remedy this, we use another model structure on sSet2 defined in the article of Cegarra and Remedios [3], which is equivalent to the Moerdijk structure. So we build a second new model structure on [Δop,Cat], which is cofibrantly generated, left proper, cellular and (co)tensored on sSet in a compatible way. Based on the work of [13], we construct the stable category of spectra (not symmetric) SpN(sCat*, Σ). It garantees the existence of Ω-spectra, which allows us to define thenotion of Waldhausen category. The calculation of the simplicial enrichment map of the model category SpN(sCat*, Σ), leads to our new definition of algebraic K-theory of weak Waldhausen categories . The second part of this thesis is an attempt to generalize the previous results for enriched categories. First we begin by recalling the theory of ∞-categories and ∞-groupoids, based on the work of Joyal [14] and Lurie [18]. Then we make comparisons of ∞-categories with the category of simplicial sets equipped with the usual model structure. Our first result is the construction of a model structure on Top – Cat , the category of small categories enriched over the category of topological spaces Top, based on the work of Bergner [1] . The category Top – Cat is Quillen equivalent to sSet – Cat. Note that all objects in Top – Cat are fibrant ; this remark will play an important role in this theory. Our second result is the construction of a new model structure on the category of small simplicial categories enriched over Top, denoted by Top – sCat = [Δop,Top – Cat]. We show that this structure is proper and cellular. The fact that Top – sCat is not (co)tensored over sSet poses a barrier to defining the category of spectra SpN(sCat*, Σ).

During the last two decades, China's food supply and demand has been a hot topic for both politicians and academics given China's rapid economic development and its sheer market size. Accordingly, researchers are trying to project the future development of China's food economy. This article reviews several influential projection models and compares their model structure, major assumptions and projection results. In addition, the author tries to pinpoint the most signiflcant factors that could influence the projection results. Several emerging issues, such as the projection Validity, livestock structure changes and data reliability are discussed at the end.

When formulating universal properties for objects in a dagger category, one usually expects a universal property to characterize the universal object up to unique unitary isomorphism. We observe that this is automatically the case in the important special case of C$^*$-categories, provided that one uses enrichment in Banach spaces. We then formulate such a universal property for infinite direct sums in C$^*$-categories, and prove the equivalence with the existing definition due to Ghez, Lima and Roberts in the case of W$^*$-categories. These infinite direct sums specialize to the usual ones in the category of Hilbert spaces, and more generally in any W$^*$-category of normal representations of a W$^*$-algebra. Finding a universal property for the more general case of direct integrals remains an open problem.

Thurston introduced a technique for finding and deforming three-dimensional hyperbolic structures by gluing together ideal tetrahedra. We generalize this technique to study families of geometric structures that transition from hyperbolic to anti-de Sitter (AdS) geometry. Our approach involves solving Thurston's gluing equations over several different shape parameter algebras. In the case of a punctured torus bundle with Anosov monodromy, we identify two components of real solutions for which there are always nearby positively oriented solutions over both the complex and pseudo-complex numbers. These complex and pseudo-complex solutions define hyperbolic and AdS structures that, after coordinate change in the projective model, may be arranged into one continuous family of real projective structures. We also study the rigidity properties of certain AdS structures with tachyon singularities.

Health Policy Model: Long-Term Predictive Results Associated with the Management of HCV-Induced Diseases in Italy

We extend the classical notion of a Reedy category so as to allow non-trivial automorphisms. Our extension includes many important examples occurring in topology such as Segal’s category Γ, or the total category of a crossed simplicial group such as Connes’ cyclic category Λ. For any generalized Reedy category $${\mathbb {R}}$$ and any cofibrantly generated model category $${{\mathcal{E}}}$$ , the functor category $${{\mathcal{E}}^\mathbb {R}}$$ is shown to carry a canonical model structure of Reedy type.

This paper describes the structure of the LAND USE SCANNER model, a GIS based model developed to generate spatial forecasts for various types of land use for a large number of grids. The model basically allocates land according to bid prices for various types of land use. The possibility of government intervention in land use is taken into account among others by adding aggregate constraints. The model includes all relevant land use types such as residential, industrial, agricultural, natural areas and water. The model is driven by sectoral models providing forecasts of aggregate land use in various land use categories. An application of the first version of the model is given for the Netherlands with some 200,000 grid cells. Further developments and refinements of the model are planned for the near future.

Variance across participants is at the heart of the centuries-old debate about the universality of beauty. Beauty's belonging to the eye of the beholder implies large interindividual variance, while beauty as a universal object property implies the opposite. To characterize the variance at the center of this debate, we selected two quartets with either high- or low-variance images with high typicality and a given mean beauty. The quartets have high or low variance across 50 participants (group variance) and correspondingly high or low variance across images of a quartet for each participant (quartet variance). We asked 52 new participants to estimate their own mean and quartet variance. Participants successfully predicted their quartet mean but failed to predict their quartet variance. Though invisible, beauty variance is essential to prediction, both in theory and in practice. The quartets show that mean beauty is not the whole story - beauty variance is heterogeneous.

SummaryThe complexity of data and methods in industrial ecology (IE) keeps growing, and the demand for comprehensive and interdisciplinary assessments increases. To keep up with this development, the field needs a data infrastructure that allows researchers to annotate, store, retrieve, combine, and exchange data at low cost, without loss of information, and across disciplines and model frameworks. A consensus‐building debate about how to describe the common object of study, socioeconomic metabolism (SEM), is necessary for the development of practical data structures and databases. We review the definitions of basic concepts to describe SEM in IE and related fields such as integrated assessment modeling. We find that many definitions are not compatible, are implicit, and are sometimes lacking. To resolve the conflicts and inconsistencies within the current definitions, we propose a hierarchical system of terms and definitions, apractical ontology, for describing objects, their properties, and events in SEM. We propose a typology of object properties and usesetsto group objects into a hierarchical, mutually exclusive, and collectively exhaustive (H‐MECE) classification. This grouping leads to a general definition ofstocks. We show that a MECE representation of events necessarily requires two complementary concepts:processesandflows, for which we propose general definitions based on sets. Using these definitions, we show that the system structure of any interdisciplinary model of SEM can be formulated as adirected graph. We propose guidelines for semantic data annotation and database design, which can help to turn the vision of a powerful data infrastructure for SEM research into reality.