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Advances in mathematics (New York. 1965), ISSN 0001-8708, 2016, Volume 302, pp. 869 - 1043
Journal Article
Theory and Applications of Categories, ISSN 1201-561X, 01/2018, Volume 33, pp. 43 - 66
In this paper, we study properties of maps between fibrant objects in model categories... 
Fibrant objects | Quillen model structures | MATHEMATICS | MATHEMATICS, APPLIED | fibrant objects
Journal Article
Applied categorical structures, ISSN 1572-9095, 2017, Volume 26, Issue 1, pp. 29 - 46
Journal Article
Applied categorical structures, ISSN 1572-9095, 2018, Volume 27, Issue 1, pp. 1 - 21
We give an account of Bousfield localisation and colocalisation for one-dimensional model categories... 
Geometry | Convex and Discrete Geometry | Bousfield (co)localisation | Mathematics | Theory of Computation | 18A40 | Primary 55U35 | Mathematical Logic and Foundations | Quillen model structures | MATHEMATICS | FACTORIZATION
Journal Article
Journal of K-Theory, ISSN 1865-2433, 10/2011, Volume 8, Issue 2, pp. 183 - 221
A Quillen model structure on the category Gray-Cat of Gray-categories is described, for which the weak equivalences are the triequivalences... 
Quillen model category | Gray-category | Enriched category | Homotopy 3-types | MATHEMATICS | enriched category | homotopy 3-types
Journal Article
Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2011, Volume 63, Issue 2, pp. 503 - 524
Journal Article
Applied Categorical Structures, ISSN 0927-2852, 12/2011, Volume 19, Issue 6, pp. 901 - 938
We extend a result of Cisinski on the construction of cofibrantly generated model structures from (Grothendieck... 
Geometry | Weak factorization system | 18C35 | 55U35 | Convex and Discrete Geometry | Homotopy | Quillen model category | Mathematics | Theory of Computation | 18G55 | Mathematical Logic and Foundations | MATHEMATICS
Journal Article
Advances in mathematics (New York. 1965), ISSN 0001-8708, 10/2016, Volume 302, p. 869
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2009, Volume 361, Issue 10, pp. 5601 - 5614
We give an explicit Lie model for any component of the space of free and pointed sections of a nilpotent fibration, and in particular, of the free and pointed mapping spaces... 
Morphisms | Algebra | Mathematical theorems | Homotopy theory | Maps | Functors | Mathematical models | Vector space models | Vector spaces | Rational homotopy theory | Space of sections | Mapping space | Sullivan model | Quillen model | SPACE | MATHEMATICS | mapping space | RATIONAL HOMOTOPY-THEORY | rational homotopy theory
Journal Article
Topology and its Applications, ISSN 0166-8641, 2008, Volume 155, Issue 5, pp. 412 - 432
We prove that the homotopy theory of parametrized spaces embeds fully and faithfully in the homotopy theory of simplicial presheaves, and that its essential... 
Homotopy sheaves | Parametrized spaces | Base change | Model category | Fibration | Ex-spaces | Right Quillen embedding | Simplicial presheaves | MATHEMATICS | MATHEMATICS, APPLIED | parametrized spaces | CATEGORY | fibration | base change | ex-spaces | homotopy sheaves | right Quillen embedding | simplicial presheaves | model category | Mathematics - Algebraic Topology
Journal Article
Applied categorical structures, ISSN 1572-9095, 2019, Volume 27, Issue 5, pp. 549 - 566
We study the category of Reedy diagrams in a $$\mathscr {V}$$ V -model category. Explicitly, we show that if K is a small category, $$\mathscr {V... 
Module over a symmetric monoidal model category | Quillen model category | Mathematics | Theory of Computation | 18D15 | Geometry | 18D10 | 19D23 | Symmetric monoidal category | 55U35 | Convex and Discrete Geometry | Reedy model structure | Mathematical Logic and Foundations | MATHEMATICS | Olefins | Analysis | Models | Mathematics - Algebraic Topology
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2019, Volume 223, Issue 7, pp. 2948 - 2976
The subject of this paper is the higher structure of the strictification adjunction, which relates the two fundamental bases of three-dimensional category... 
MATHEMATICS | MATHEMATICS, APPLIED | QUILLEN MODEL STRUCTURE | CATEGORIES | Mathematics - Category Theory
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 2011, Volume 269, Issue 3-4, pp. 977 - 1004
...’ cyclic category Λ. For any generalized Reedy category R and any cofibrantly generated model category , the functor category R is shown to carry a canonical model... 
Generalized Reedy category | Crossed group | 55U35 | Dendroidal set | 20N99 | Quillen model category | Secondary 18G30 | Mathematics, general | Mathematics | Primary 18G55 | MATHEMATICS | MODELS | SPACES | COMPLEXES | HOMOTOPY-THEORY | HOMOLOGY | DENDROIDAL SETS
Journal Article
Applied categorical structures, ISSN 1572-9095, 2019, Volume 27, Issue 3, pp. 311 - 322
In this article, the author endows the functor category [B(Z2),Gpd] with the structure of a type-theoretic fibration category with a univalent universe, using the so-called injective model structure... 
Groupoid | Type-theoretic fibration category | Univalent Foundations | Homotopy Type Theory | Quillen model category | Universe | Groupoid model | Univalence Axiom | Injective model structure | Model invariance problem | MATHEMATICS | UNIVALENCE | Computer science | Gates, Bill | Analysis
Journal Article
K-Theory, ISSN 0920-3036, 11/2004, Volume 33, Issue 3, pp. 185 - 197
A cofibrantly generated Quillen model structure on the category Bicats, of bicategories and strict homomorphisms is constructed... 
Geometry | Algebra | Analysis | Quillen model | Mathematics | Group Theory and Generalizations | Bicat s | 2-Cat | Bicat | MATHEMATICS | Bicats | CATEGORIES
Journal Article
Communications in Algebra, ISSN 0092-7872, 04/2019, Volume 47, Issue 4, pp. 1708 - 1730
.... We also construct on the category of complexes several model structures from modules and complexes with finite FP n -injective and FP n -flat dimensions, and analyze some situations where it is... 
cover | cotorsion pair | Quillen equivalence | model structure | preenvelope | Complex | 18G15 | 16E05 | COVERS | 18G55 | 16E35 | 18G35 | MATHEMATICS | 16E10 | MODULES | DIMENSION | COTORSION PAIRS | Homology | Construction
Journal Article
Theory and Applications of Categories, ISSN 1201-561X, 2005, Volume 15, Issue 3
Journal Article
Chinese Annals of Mathematics, Series B, ISSN 0252-9599, 1/2016, Volume 37, Issue 1, pp. 95 - 102
There are various adjunctions between model (co)slice categories. The author gives a proposition to characterize when these adjunctions are Quillen equivalences... 
Model slice categories | 18A25 | Homotopy categories | Quillen equivalences | 55U35 | 18E30 | Mathematics, general | Mathematics | Applications of Mathematics | 18G55 | MATHEMATICS
Journal Article
Journal of Homotopy and Related Structures, ISSN 2193-8407, 09/2015, Volume 10, Issue 3, pp. 549 - 564
... to . Let denote the group of homotopy self-equivalences of the -localization . We use DG Lie models to construct a short exact sequence where is a... 
Homotopy self-equivalences | Anick model | (Formula presented.) -local homotopy theory Moore space | Nilpotent group | Quillen model | MATHEMATICS | R-local homotopy theory Moore space | HOMOTOPY-EQUIVALENCES | NILPOTENCY
Journal Article
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