A Categorical approach to Tannaka Duality
The aim of this work is to study, in a categorical context, similar results to the Tannaka-Krein duality theorem. We prove a reconstruction theorem which allows one to recover a given group G as the monoid of natural endomorphisms of the forgetful functor from its category of permutation representat...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/89880 |
| Acceso en línea: | https://hdl.handle.net/2117/89880 |
| Access Level: | acceso abierto |
| Palabra clave: | Categories (Mathematics) Representation theory Tannaka duality Yoneda lemma Enriched category Symmetric monoidal closed category Reconstruction Monoid Categories (Matemàtica) Classificació AMS::18 Category theory homological algebra::18D Categories with structure Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de categories àlgebra homològica |
| Sumario: | The aim of this work is to study, in a categorical context, similar results to the Tannaka-Krein duality theorem. We prove a reconstruction theorem which allows one to recover a given group G as the monoid of natural endomorphisms of the forgetful functor from its category of permutation representations to Set. The proof of this result follows as a consequence of the Yoneda lemma. After introducing some necessary categorical concepts and results, and introducing the context of enriched category theory and the enriched version of the Yoneda lemma, we prove the enriched version of the reconstruction theorem for a general monoid A in a symmetric monoidal closed category V, which is recovered as the monoid in V of enriched natural endomorphisms of the forgetful V-functor from the enriched category of representations of A to V. |
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