dc.contributor |
Centre de Recerca Matemàtica |
dc.contributor.author |
Faro, Emilio |
dc.date.accessioned |
2009-04-27T07:30:12Z |
dc.date.available |
2009-04-27T07:30:12Z |
dc.date.created |
2008-10 |
dc.date.issued |
2008-10 |
dc.identifier.uri |
http://hdl.handle.net/2072/15542 |
dc.format.extent |
30 |
dc.format.extent |
373006 bytes |
dc.format.mimetype |
application/pdf |
dc.language.iso |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation.ispartofseries |
Prepublicacions del Centre de Recerca Matemàtica;833 |
dc.rights |
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 (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) |
dc.subject.other |
Categories (Matemàtica) |
dc.title |
On the trace of an endofunctor of a small category |
dc.type |
info:eu-repo/semantics/preprint |
dc.subject.udc |
512 - Àlgebra |
dc.description.abstract |
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. |