Título:
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On the trace of an endofunctor of a small category
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Autor/a:
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Faro, Emilio; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
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Abstract:
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The trace of a square matrix can be defined by a universal property which, appropriately generalized yields the concept of "trace of an endofunctor of a small category". We review the basic definitions of this general concept and give a new construction, the "pretrace category", which allows us to obtain the trace of an endofunctor of a small category as the set of connected components of its pretrace. We show that this pretrace construction determines a finite-product preserving endofunctor of the category of small categories, and we deduce from this that the trace inherits any finite-product algebraic structure that the original category may have. We apply our results to several examples from Representation Theory obtaining a new (indirect) proof of the fact that two finite dimensional linear representations of a finite group are isomorphic if and only if they have the same character. |
Materia(s):
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-Categories (Matemàtica) |
Derechos:
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open access
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús
https://creativecommons.org/licenses/by-nc-nd/2.5/ |
Tipo de documento:
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Article Prepublicació |
Editor:
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Centre de Recerca Matemàtica
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Compartir:
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Uri:
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https://ddd.uab.cat/record/44451
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