Related papers: Right Delocalization of Model Categories
There are many ways to present model categories, each with a different point of view. Here we'd like to treat model categories as a way to build and control resolutions. This an historical approach, as in his original and spectacular…
Building on structure observed in equivariant homotopy theory, we define an equivariant generalization of a symmetric monoidal category: a $G$-symmetric monoidal category. These record not only the symmetric monoidal products but also…
Small B\'{e}nabou's bicategories and, in particular, Mac Lane's monoidal categories, have well-understood classifying spaces, which give geometric meaning to their cells. This paper contains some contributions to the study of the…
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…
In this thesis we define the notion of a locally stratified space. Locally stratified spaces are particular kinds of streams and d-spaces which are locally modelled on stratified spaces. We construct a locally presentable and cartesian…
In order to apply nonstandard methods to questions of algebraic geometry we continue our investigation from "Enlargements of categories" (Theory Appl. Categ. 14 (2005), No. 16, 357--398) and show how important homotopical constructions…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to…
In Bayesian classification, it is important to establish a probabilistic model for each class for likelihood estimation. Most of the previous methods modeled the probability distribution in the whole sample space. However, real-world…
Orthogonality is a notion based on the duality between programs and their environments used to determine when they can be safely combined. For instance, it is a powerful tool to establish termination properties in classical formal systems.…
Multilevel or hierarchical data structures can occur in many areas of research, including economics, psychology, sociology, agriculture, medicine, and public health. Over the last 25 years, there has been increasing interest in developing…
For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…
A Quillen model structure is presented by an interacting pair of weak factorization systems. We prove that in the world of locally presentable categories, any weak factorization system with accessible functorial factorizations can be lifted…
In \cite{CompTheo} we studied the indeterminacy of the value of a derived functor at an object using different definitions of a derived functor and different types of fibrant replacement. In the present work we focus on derived or homotopy…
Category theory has been successfully applied in various domains of science, shedding light on universal principles unifying diverse phenomena and thereby enabling knowledge transfer between them. Applications to machine learning have been…
Trained using only image class label, deep weakly supervised methods allow image classification and ROI segmentation for interpretability. Despite their success on natural images, they face several challenges over histology data where ROI…
This case study is an update-in-place refactoring transformation on UML class diagrams. Its aim is to remove clones of attributes from a class diagram, and to identify new classes which abstract groups of classes that share common data…
Fix a prime $p$. Since their definition in the context of Localization Theory, the homotopy functors $P_{B\Z/p}$ and $CW_{B\Z/p}$ have shown to be powerful tools to understand and describe the mod $p$ structure of a space. In this paper, we…
The invertibility hypothesis for a monoidal model category S asks that localizing an S-enriched category with respect to an equivalence results in an weakly equivalent enriched category. This is the most technical among the axioms for S to…
Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…