Model Categories and Bousfield Localization

2019 ◽  
pp. 71-84
Author(s):  
Tobias Dyckerhoff ◽  
Mikhail Kapranov
Keyword(s):  
Model Categories ◽  
Bousfield Localization

Model Structures for the 𝔸1-homotopy Category

2019 ◽  
pp. 175-212
Author(s):  
Christian Haesemeyer ◽  
Charles A. Weibel
Keyword(s):  
Full Subcategory ◽  
Homotopy Category ◽  
Symmetric Power ◽  
Model Structure ◽  
Model Categories ◽  
Simplicial Presheaves ◽  
Basic Ideas ◽  
Quillen Model ◽  
Model Structures ◽  
Bousfield Localization

This chapter provides the 𝔸1-local projective model structure on the categories of simplicial presheaves and simplicial presheaves with transfers. These model categories, written as Δ‎opPshv(Sm)𝔸1 and Δ‎op PST(Sm)𝔸1, are first defined. Their respective homotopy categories are Ho(Sm) and the full subcategory DM eff nis ≤0 of DM eff nis. Afterward, this chapter introduces the notions of radditive presheaves and ̅Δ‎-closed classes, and develops their basic properties. The theory of ̅Δ‎-closed classes is needed because the extension of symmetric power functors to simplicial radditive presheaves is not a left adjoint. This chapter uses many of the basic ideas of Quillen model categories, which is a category equipped with three classes of morphisms satisfying five axioms. In addition, much of the material in this chapter is based upon the technique of Bousfield localization.

scholarly journals Locally constant functors

2009 ◽  
Vol 147 (3) ◽  
pp. 593-614 ◽  
Author(s):  
DENIS–CHARLES CISINSKI
Keyword(s):  
Homotopy Theory ◽  
Model Category ◽  
Model Categories ◽  
Combinatorial Model ◽  
Constant Coefficients ◽  
Kan Extensions ◽  
Bousfield Localization

AbstractWe study locally constant coefficients. We first study the theory of homotopy Kan extensions with locally constant coefficients in model categories, and explain how it characterizes the homotopy theory of small categories. We explain how to interpret this in terms of left Bousfield localization of categories of diagrams with values in a combinatorial model category. Finally, we explain how the theory of homotopy Kan extensions in derivators can be used to understand locally constant functors.

Equivariant Topology and Derived Algebra

2021 ◽  
Keyword(s):  
Homotopy Theory ◽  
Algebraic Models ◽  
Research Papers ◽  
Model Categories ◽  
Homotopy Limits ◽  
Equivariant Topology ◽  
Mackey Functors ◽  
Chromatic Homotopy ◽  
Equivariant Spectra ◽  
Bousfield Localization

This volume contains eight research papers inspired by the 2019 'Equivariant Topology and Derived Algebra' conference, held at the Norwegian University of Science and Technology, Trondheim in honour of Professor J. P. C. Greenlees' 60th birthday. These papers, written by experts in the field, are intended to introduce complex topics from equivariant topology and derived algebra while also presenting novel research. As such this book is suitable for new researchers in the area and provides an excellent reference for established researchers. The inter-connected topics of the volume include: algebraic models for rational equivariant spectra; dualities and fracture theorems in chromatic homotopy theory; duality and stratification in tensor triangulated geometry; Mackey functors, Tambara functors and connections to axiomatic representation theory; homotopy limits and monoidal Bousfield localization of model categories.

scholarly journals On the construction of functorial factorizations for model categories

2013 ◽  
Vol 13 (2) ◽  
pp. 1089-1124 ◽  
Author(s):  
Tobias Barthel ◽  
Emily Riehl
Keyword(s):  
Model Categories

Model Categories

2009 ◽  
pp. 65-138
Author(s):  
Paul G. Goerss ◽  
John F. Jardine
Keyword(s):  
Model Categories

Reedy model categories

1999 ◽  
pp. 353-387 ◽  
Author(s):  
Paul G. Goerss ◽  
John F. Jardine
Keyword(s):  
Model Categories

scholarly journals The Scoring Mechanism of Players after Game Based on Cluster Regression Analysis Model

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jin Xu ◽  
Chao Yi
Keyword(s):  
Regression Analysis ◽  
Regression Model ◽  
Regression Models ◽  
Effective Theory ◽  
Standard Errors ◽  
Limited Data ◽  
Analysis Model ◽  
Multiple Objects ◽  
Model Categories ◽  
Model Expression

Cluster regression analysis model is an effective theory for a reasonable and fair player scoring game. It can roughly predict and evaluate the performance of athletes after the game with limited data and provide scientific predictions for the performance of athletes. The purpose of this research is to achieve the player’s postmatch scoring through the cluster regression model. Through the research and analysis of past ball games, the comparison and experiment of multiple objects based on different regression analysis theories, the following conclusions are drawn. Different regression models have different standard errors, but if the data in other model categories are put into the centroid model expression, the standard error and the error of the original model are within 0.3, which can replace other models for calculation. In the player’s postmatch scoring, although the expert’s prediction of the result is very accurate, within the error range of 1 copy, the player’s postmatch scoring mechanism based on the cluster regression analysis model is more accurate, and the error formula is in the 0.5 range. It is best to switch the data of the regression model twice to compare the scoring mechanism using different regression experiments.

scholarly journals Obstruction theory in model categories

2004 ◽  
Vol 181 (2) ◽  
pp. 396-416 ◽  
Author(s):  
J.Daniel Christensen ◽  
William G. Dwyer ◽  
Daniel C. Isaksen
Keyword(s):  
Obstruction Theory ◽  
Model Categories
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