Results 11 to 20 of about 6,556,269 (259)
Chromatic structures in stable homotopy theory [PDF]
Handbook of Homotopy Theory, 2019 In this survey, we review how the global structure of the stable homotopy category gives rise to the chromatic filtration. We then discuss computational tools used in the study of local chromatic homotopy theory, leading up to recent developments in the ...
T. Barthel, A. Beaudry
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Homotopy theory of homotopy algebras [PDF]
Annales de l'Institut Fourier, 2020 This paper studies the homotopy theory of algebras and homotopy algebras over an operad. It provides an exhaustive description of their higher homotopical properties using the more general notion of morphism called infinity-morphism. The method consists in using the operadic calculus to endow the category of coalgebras over the Koszul dual cooperad or ...
Vallette, Bruno
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Cubical synthetic homotopy theory [PDF]
Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, 2020 Homotopy type theory is an extension of type theory that enables synthetic reasoning about spaces and homotopy theory. This has led to elegant computer formalizations of multiple classical results from homotopy theory.
Anders Mörtberg, Lo¨ıc Pujet
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Three models for the homotopy theory of homotopy theories
Topology, 2007 Given any model category, or more generally any category with weak equivalences, its simplicial localization is a simplicial category which can rightfully be called the "homotopy theory" of the model category. There is a model category structure on the category of simplicial categories, so taking its simplicial localization yields a "homotopy theory of
Bergner, Julia E.
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Two Models for the Homotopy Theory of Cocomplete Homotopy Theories [PDF]
, 2014 We prove that the homotopy theory of cofibration categories is equivalent to the homotopy theory of cocomplete quasicategories. This is achieved by presenting both homotopy theories as fibration categories and constructing an explicit equivalence between them.
Szumilo, K. +2 more
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Quantum Gauge Field Theory in Cohesive Homotopy Type Theory [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We implement in the formal language of homotopy type theory a new set of axioms called cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in quantum gauge field theory.
Urs Schreiber, Michael Shulman
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Homotopy Transfer and Effective Field Theory I: Tree‐level [PDF]
Fortschritte der Physik, 2020 We use the dictionary between general field theories and strongly homotopy algebras to provide an algebraic formulation of the procedure of integrating out of degrees of freedom in terms of homotopy transfer. This includes more general effective theories
Alex S. Arvanitakis +3 more
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2-adjoint equivalences in homotopy type theory [PDF]
Logical Methods in Computer Science, 2021 We introduce the notion of (half) 2-adjoint equivalences in Homotopy Type Theory and prove their expected properties. We formalized these results in the Lean Theorem Prover.
Daniel Carranza +3 more
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Modern Birkhäuser Classics, 2009 Simplicial sets.- Model Categories.- Classical results and constructions.- Bisimplicial sets.- Simplicial groups.- The homotopy theory of towers.- Reedy model categories.- Cosimplicial spaces: applications.- Simplicial functors and homotopy coherence.- Localization.
P. Goerss, J. Jardine
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On the Nielsen-Schreier Theorem in Homotopy Type Theory [PDF]
Logical Methods in Computer Science, 2022 We give a formulation of the Nielsen-Schreier theorem (subgroups of free groups are free) in homotopy type theory using the presentation of groups as pointed connected 1-truncated types.
Andrew W Swan
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