Search results for "Homotopia"

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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Pintojen perusryhmistä

2015

Tässä tutkielmassa osoitetaan ennestään tunnettu pintoihin liittyvä tulos, jonka mukaan epäkompaktin pinnan perusryhmä on vapaa. Todistus pohjautuu tietoon siitä, että jokaisella pinnalla on olemassa niin sanottu kolmiointi. Pinnan kolmiointia hyödyntäen pinta tyhjennetään sopivilla sisäkkäisillä kompakteilla reunallisilla pinnoilla siten, että pinnan perus ryhmä saadaan näiden kompaktien reunallisten pintojen sisäkkäisten pe rusryhmien yhdisteenä. Kompakti reunallinen pinta osoitetaan homotopia ekvivalentiksi graafin kanssa deformaatioretraktoimalla reunallinen pinta graafiksi reunallisen pinnan kolmiointia hyödyntäen. Koska homotopiaekvi valenttien avaruuksien perusryhmät ovat isomorfiset…

pintahomotopiapinnatgraafivapaa ryhmätopologiaalgebrallinen topologiaryhmätgraafitperusryhmä
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Weighted limits in simplicial homotopy theory

2010

Abstract By combining ideas of homotopical algebra and of enriched category theory, we explain how two classical formulas for homotopy colimits, one arising from the work of Quillen and one arising from the work of Bousfield and Kan, are instances of general formulas for the derived functor of the weighted colimit functor.

Pure mathematicsAlgebra and Number TheoryFunctorBrown's representability theoremHomotopy categoryModel categoryHomotopical algebraHomotopiaQuillen adjunctionCone (category theory)Mathematics::Algebraic TopologyAlgebraCategories (Matemàtica)Homotopy limits simplicial model categories weighted limitsMathematics::K-Theory and HomologyMathematics::Category TheorySimplicial set512 - ÀlgebraMathematics
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The identity type weak factorisation system

2008

We show that the classifying category C(T) of a dependent type theory T with axioms for identity types admits a non-trivial weak factorisation system. We provide an explicit characterisation of the elements of both the left class and the right class of the weak factorisation system. This characterisation is applied to relate identity types and the homotopy theory of groupoids.

Class (set theory)Pure mathematicsGeneral Computer ScienceDependent type theoryHomotopiaType (model theory)Identity (music)Theoretical Computer Science510 - Consideracions fonamentals i generals de les matemàtiquesCombinatorics18C50Mathematics::Category TheoryFOS: MathematicsCategory Theory (math.CT)Univalent foundationsAxiomMathematicsHomotopy03B15; 18C50; 18B40Mathematics - Category TheoryIdentity type weak factorisation systemMathematics - LogicTipus Teoria dels03B15Type theory18B40Homotopy type theoryLogic (math.LO)Weak factorisation systemIdentity typeComputer Science(all)
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