Advances in mathematics (New York. 1965), ISSN 0001-8708, 2016, Volume 302, pp. 869 - 1043

... between the respective model categories.

Simplicial operads | Infinity-operads | Forest sets | Dendroidal sets | Quillen equivalence | Quillen model structures | MATHEMATICS | SETS | HOMOTOPY-THEORY | CATEGORIES

Simplicial operads | Infinity-operads | Forest sets | Dendroidal sets | Quillen equivalence | Quillen model structures | MATHEMATICS | SETS | HOMOTOPY-THEORY | CATEGORIES

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

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

We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category...

Mathematics | Theory of Computation | Localization of a model structure | 18G55 | Stable homotopy category | Geometry | 18D10 | Symmetric spectra | Stable model structure | Symmetric monoidal model category | Convex and Discrete Geometry | Quillen functors | Cofibrantly generated model category | Mathematical Logic and Foundations | MATHEMATICS | HOMOTOPY | CATEGORIES

Mathematics | Theory of Computation | Localization of a model structure | 18G55 | Stable homotopy category | Geometry | 18D10 | Symmetric spectra | Stable model structure | Symmetric monoidal model category | Convex and Discrete Geometry | Quillen functors | Cofibrantly generated model category | Mathematical Logic and Foundations | MATHEMATICS | HOMOTOPY | CATEGORIES

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

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

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

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

Applied Categorical Structures, ISSN 0927-2852, 8/2010, Volume 18, Issue 4, pp. 343 - 375

For every closed model category with zero object, Quillen gave the construction of Eckman-Hilton and Puppe sequences...

Cofibration sequence | Steenrod homotopy group | Proper homotopy | Quillen model category | Fibration sequence | Mathematics | Theory of Computation | 55Q70 | Brown-Grossman homotopy group | Geometry | 55U35 | 55U40 | 55N25 | Convex and Discrete Geometry | Model category with non-zero object | Exterior space | Shape theory | Mathematical Logic and Foundations | Group cohomology | Brown-grossman homotopy group | SPACES | PROPER HOMOTOPY-THEORY | MATHEMATICS

Cofibration sequence | Steenrod homotopy group | Proper homotopy | Quillen model category | Fibration sequence | Mathematics | Theory of Computation | 55Q70 | Brown-Grossman homotopy group | Geometry | 55U35 | 55U40 | 55N25 | Convex and Discrete Geometry | Model category with non-zero object | Exterior space | Shape theory | Mathematical Logic and Foundations | Group cohomology | Brown-grossman homotopy group | SPACES | PROPER HOMOTOPY-THEORY | MATHEMATICS

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 10/2016, Volume 302, p. 869

... between the respective model categories.

Infinity-operads | Dendroidal sets | Quillen equivalence | Mathematics(all) | Simplicial operads | Forest sets | Quillen model structures

Infinity-operads | Dendroidal sets | Quillen equivalence | Mathematics(all) | Simplicial operads | Forest sets | Quillen model structures

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

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

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

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

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

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

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

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

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

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

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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