Algebraic and Geometric Topology, ISSN 1472-2747, 2019, Volume 19, Issue 3, pp. 1171 - 1206

In recent years the theory of dendroidal sets has emerged as an important framework for higher algebra...

MATHEMATICS | NONCOMMUTATIVE SPECTRA | MODEL STRUCTURE | HOMOTOPY-THEORY | COMPLEXES

MATHEMATICS | NONCOMMUTATIVE SPECTRA | MODEL STRUCTURE | HOMOTOPY-THEORY | COMPLEXES

Journal Article

2016, ISBN 9781470427245, xiv, 352 pages

Book

NEW YORK JOURNAL OF MATHEMATICS, ISSN 1076-9803, 2019, Volume 25, pp. 627 - 641

We show that the category of simplicial sets is a co-reflective subcategory of the category of cubical sets with connections, with the inclusion given by a version of the straightening functor...

cubical sets | MATHEMATICS | model categories | simplicial sets | (infinity, 1)-categories

cubical sets | MATHEMATICS | model categories | simplicial sets | (infinity, 1)-categories

Journal Article

Computer Aided Geometric Design, ISSN 0167-8396, 05/2018, Volume 62, pp. 44 - 62

Simplicial sets and cubical sets are combinatorial structures which have been studied for a long time in Algebraic Topology...

Bézier simploids | Simplicial sets | Cubical sets | Simploidal sets | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Bezier simploids | Graphics software | Usage | Analysis

Bézier simploids | Simplicial sets | Cubical sets | Simploidal sets | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Bezier simploids | Graphics software | Usage | Analysis

Journal Article

2015, Mathematical surveys and monographs, ISBN 9781470425456, Volume no. 209., viii, 218

Book

Journal of Algebra and its Applications, ISSN 0219-4988, 01/2019, Volume 18, Issue 1

In rough set theory (RST), the notion of decision table plays a fundamental role...

decision systems | Rough set theory | abstract simplicial complexes | set operators | closure systems | set partitions | MATHEMATICS, APPLIED | PRECLUSIVITY | EXTENSION | NEGATIVE TYPE | GRAPHS | MATHEMATICS | FINITE METRIC-SPACES | HYPERGRAPH | LATTICES

decision systems | Rough set theory | abstract simplicial complexes | set operators | closure systems | set partitions | MATHEMATICS, APPLIED | PRECLUSIVITY | EXTENSION | NEGATIVE TYPE | GRAPHS | MATHEMATICS | FINITE METRIC-SPACES | HYPERGRAPH | LATTICES

Journal Article

Physical review letters, ISSN 1079-7114, 2010, Volume 104, Issue 18, p. 181301

A one parameter family of retarded linear operators on scalar fields on causal sets is introduced...

SPACE-TIME | PHYSICS, MULTIDISCIPLINARY | SIMPLICIAL QUANTUM-GRAVITY | SPACE | LORENTZ INVARIANCE | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | MATHEMATICAL SPACE | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | SCALAR FIELDS | QUANTUM OPERATORS | MATHEMATICAL OPERATORS | CAUSALITY | MINKOWSKI SPACE | INVARIANCE PRINCIPLES

SPACE-TIME | PHYSICS, MULTIDISCIPLINARY | SIMPLICIAL QUANTUM-GRAVITY | SPACE | LORENTZ INVARIANCE | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | MATHEMATICAL SPACE | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | SCALAR FIELDS | QUANTUM OPERATORS | MATHEMATICAL OPERATORS | CAUSALITY | MINKOWSKI SPACE | INVARIANCE PRINCIPLES

Journal Article

1995, ISBN 9789810221379, xvi, 356

Book

Journal of Homotopy and Related Structures, ISSN 2193-8407, 12/2019, Volume 14, Issue 4, pp. 1043 - 1082

...}}$$ C -diagrams of simplicial sets, for a small index category $${\mathcal {C}}$$ C . When $${\mathcal {C}}$$ C is an EI-category satisfying some mild finiteness restrictions, we show that every fibration...

Algebra | Functional Analysis | Fibre bundle | Simplicial space | Minimal fibration | Algebraic Topology | Mathematics | Number Theory | Diagram | MATHEMATICS

Algebra | Functional Analysis | Fibre bundle | Simplicial space | Minimal fibration | Algebraic Topology | Mathematics | Number Theory | Diagram | MATHEMATICS

Journal Article

The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2012, Volume 42, Issue 2, pp. 353 - 423

This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins...

Morphisms | Equivalence relation | Homotopy theory | Maps | Axioms | Functors | Mathematics | Algebraic topology | Vertices | Topological spaces | Simplicial sets | Simplicial homotogy | MATHEMATICS | simplicial homotopy | 18G30 | 55U10

Morphisms | Equivalence relation | Homotopy theory | Maps | Axioms | Functors | Mathematics | Algebraic topology | Vertices | Topological spaces | Simplicial sets | Simplicial homotogy | MATHEMATICS | simplicial homotopy | 18G30 | 55U10

Journal Article

SIAM journal on numerical analysis, ISSN 1095-7170, 2017, Volume 55, Issue 1, pp. 131 - 143

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2019, Volume 11502, pp. 213 - 226

Conference Proceeding

Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 06/2018, Volume 27, Issue 7, p. 1841013

In 2004, Carter, Elhamdadi and Saito defined a homology theory for set-theoretic Yang–Baxter operators...

Homology | pre-cubical module | torsion | Yang-Baxter operators | pre-simplicial module | MATHEMATICS | KNOT INVARIANTS | ALGEBRAIC STRUCTURES | EQUATION

Homology | pre-cubical module | torsion | Yang-Baxter operators | pre-simplicial module | MATHEMATICS | KNOT INVARIANTS | ALGEBRAIC STRUCTURES | EQUATION

Journal Article

Constructive Approximation, ISSN 0176-4276, 4/2018, Volume 47, Issue 2, pp. 357 - 371

Sharp metric entropy estimates under Hausdorff distance are obtained for classes of bounded sets with positive reach, extending a well-known result...

Star-shaped | 52A30 | Numerical Analysis | Analysis | Simplicial approximation | Mathematics | Hausdorff distance | Secondary 41A46 | Metric entropy | Primary 52C17 | Positive reach | MATHEMATICS | CONVEX-FUNCTIONS

Star-shaped | 52A30 | Numerical Analysis | Analysis | Simplicial approximation | Mathematics | Hausdorff distance | Secondary 41A46 | Metric entropy | Primary 52C17 | Positive reach | MATHEMATICS | CONVEX-FUNCTIONS

Journal Article

Applied Categorical Structures, ISSN 0927-2852, 12/2016, Volume 24, Issue 6, pp. 765 - 796

The Catalan simplicial set ℂ is known to classify skew-monoidal categories in the sense that a map from ℂ...

Geometry | Nerve | Skew monoidal | Category | Convex and Discrete Geometry | Simplicial set | Bicategory | Catalan | Monoidal | Mathematics | Theory of Computation | Mathematical Logic and Foundations | MATHEMATICS

Geometry | Nerve | Skew monoidal | Category | Convex and Discrete Geometry | Simplicial set | Bicategory | Catalan | Monoidal | Mathematics | Theory of Computation | Mathematical Logic and Foundations | MATHEMATICS

Journal Article

Journal of Applied and Industrial Mathematics, ISSN 1990-4789, 1/2017, Volume 11, Issue 1, pp. 58 - 69

A graph is called a 1-triangle if, for its every maximal independent set I, every edge of this graph with both endvertices not belonging to I is contained exactly in one triangle with a vertex...

edge-simplicial graph | perfect neighborhood set | triangle graph | NP-completeness | Mathematics, general | Mathematics | characterization | Studies | Set theory | Graph theory | Algorithms | Mathematical analysis | Triangles | Graphs | Mathematical models | Polynomials | Recognition

edge-simplicial graph | perfect neighborhood set | triangle graph | NP-completeness | Mathematics, general | Mathematics | characterization | Studies | Set theory | Graph theory | Algorithms | Mathematical analysis | Triangles | Graphs | Mathematical models | Polynomials | Recognition

Journal Article

2002, ISBN 9789812380388, xiv, 606

Book

Electronic Journal of Combinatorics, ISSN 1077-8926, 12/2012, Volume 19, Issue 4

The combinatorial Hopf algebra on building sets BSet extends the chromatic Hopf algebra of simple graphs...

Building set | Graph | Cd-index | Simplicial complex | Hopf algebra | Symmetric function | Dehn- sommerville relations | MATHEMATICS | MATHEMATICS, APPLIED | Dehn-Sommerville relations | symmetric function | simplicial complex | POLYTOPES | INDEX | graph | cd-index | building set

Building set | Graph | Cd-index | Simplicial complex | Hopf algebra | Symmetric function | Dehn- sommerville relations | MATHEMATICS | MATHEMATICS, APPLIED | Dehn-Sommerville relations | symmetric function | simplicial complex | POLYTOPES | INDEX | graph | cd-index | building set

Journal Article

19.
Full Text
On the equivalence between Lurie's model and the dendroidal model for infinity-operads

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

We compare two approaches to the homotopy theory of ∞-operads. One of them, the theory of dendroidal sets, is based on an extension of the theory of simplicial sets...

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

Discrete Applied Mathematics, ISSN 0166-218X, 2009, Volume 157, Issue 3, pp. 542 - 557

The combinatorial structure of simploidal sets generalizes both simplicial complexes and cubical complexes...

Homology | Semi-simplicial sets | Simploidal sets | Topological based modeling | TOPOLOGY | MATHEMATICS, APPLIED | HOMOTOPY THEORY | Image processing | Analysis | Equipment and supplies | Modeling and Simulation | Computer Science

Homology | Semi-simplicial sets | Simploidal sets | Topological based modeling | TOPOLOGY | MATHEMATICS, APPLIED | HOMOTOPY THEORY | Image processing | Analysis | Equipment and supplies | Modeling and Simulation | Computer Science

Journal Article

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