Search results for "Homotopy lifting property"

showing 4 items of 4 documents

Homotopy limits for 2-categories

2008

AbstractWe study homotopy limits for 2-categories using the theory of Quillen model categories. In order to do so, we establish the existence of projective and injective model structures on diagram 2-categories. Using these results, we describe the homotopical behaviour not only of conical limits but also of weighted limits. Finally, pseudo-limits are related to homotopy limits.

Discrete mathematicsPure mathematicsHomotopy lifting propertyHomotopy categoryGeneral MathematicsHomotopyHomotopiaQuillen adjunctionWhitehead theoremCofibrationMathematics::Algebraic Topologyn-connectedCategories (Matemàtica)Mathematics::K-Theory and HomologyHomotopy hypothesisMathematics::Category Theory512 - Àlgebra2-categories homotopy limits coherence conditionsMathematics
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On the proper homotopy invariance of the Tucker property

2006

A non-compact polyhedron P is Tucker if, for any compact subset K ⊂ P, the fundamental group π1(P − K) is finitely generated. The main result of this note is that a manifold which is proper homotopy equivalent to a Tucker polyhedron is Tucker. We use Poenaru’s theory of the equivalence relations forced by the singularities of a non-degenerate simplicial map.

Fundamental groupHomotopy lifting propertyApplied MathematicsGeneral MathematicsHomotopyMathematics::Optimization and ControlhomotopyproperComputer Science::Numerical AnalysisRegular homotopyCombinatoricsn-connectedPolyhedronEquivalence relationtucker propertySimplicial mapMathematics
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Discrete and differential homotopy in circular restricted three-body control

2010

The planar circular restricted three-body problem is considered. The control enters linearly in the equation of motion to model the thrust of the third body. The minimum time optimal control problem has two scalar parameters: The ratio of the primaries masses which embeds the two-body problem into the three-body one, and the upper bound on the control norm. Regular extremals of the maximum principle are computed by shooting thanks to continuations with respect to both parameters. Discrete and di erential homotopy are compared in connection with second order sucient conditions in optimal control. Homotopy with respect to control bound gives evidence of various topological structures of extr…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Homotopy lifting propertyHomotopy010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Optimal control01 natural sciencesUpper and lower boundsRegular homotopyn-connectedMaximum principle0103 physical sciences[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematics010303 astronomy & astrophysicsHomotopy analysis methodComputingMilieux_MISCELLANEOUSMathematics
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Inductive types in homotopy type theory

2012

Homotopy type theory is an interpretation of Martin-L\"of's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for intensional systems of type theory as well as a computational approach to algebraic topology via type theory-based proof assistants such as Coq. The present work investigates inductive types in this setting. Modified rules for inductive types, including types of well-founded trees, or W-types, are presented, and the basic homotopical semantics of such types are determined. Proofs of all results have been formally verified by the Coq proof assistant, and the proof s…

FOS: Computer and information sciencesComputer Science - Logic in Computer Science03B15 03B70 03F500102 computer and information sciences01 natural sciencesComputer Science::Logic in Computer ScienceFOS: MathematicsA¹ homotopy theoryCategory Theory (math.CT)0101 mathematicsMathematicsHomotopy lifting propertyType theory inductive types homotopy-initial algebraHomotopy010102 general mathematicsMathematics - Category TheoryIntuitionistic type theoryMathematics - LogicSettore MAT/01 - Logica MatematicaLogic in Computer Science (cs.LO)Algebran-connectedType theoryTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES010201 computation theory & mathematicsProof theoryTheoryofComputation_LOGICSANDMEANINGSOFPROGRAMSHomotopy type theoryComputer Science::Programming LanguagesLogic (math.LO)
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