摘要: This paper describes a relationship between essentially finite groupoids and 2-vector spaces. In particular, we show to construct spaces of Vect-valued presheaves on such groupoids. We define 2-linear maps corresponding functors in both covariant contravariant way, which are ambidextrous adjoints. is used representation--a weak functor--from Span(Gpd) (the bicategory spans groupoids) into 2Vect. this prove give the construction detail.
arxiv.org
harvard.edu
sci-hub.st 参考文章(14)
F. William Lawvere, Some algebraic problems in the context of functorial semantics of algebraic theories Springer, Berlin, Heidelberg. pp. 41- 61 ,(1968) , 10.1007/BFB0077116
Alexander E. Hoffnung, John C. Baez, Christopher D. Walker, Higher-Dimensional Algebra VII: Groupoidification arXiv: Quantum Algebra. ,(2009)
Ieke Moerdijk, Saunders MacLane Galdós, Sheaves in Geometry and Logic: A First Introduction to Topos Theory ,(2018)
John C. Baez, James Dolan, From Finite Sets to Feynman Diagrams arXiv: Quantum Algebra. pp. 29- 50 ,(2001) , 10.1007/978-3-642-56478-9_3
Ross Street, ENRICHED CATEGORIES AND COHOMOLOGY Quaestiones Mathematicae. ,vol. 6, pp. 265- 283 ,(1983) , 10.1080/16073606.1983.9632304
Shlomo Sternberg, Eugene Golowich, Group theory and physics ,(1994)
Saunders MacLane, Peter Freyd, Abelian Categories. An Introduction to the Theory of Functors. The American Mathematical Monthly. ,vol. 72, pp. 1043- ,(1965) , 10.2307/2313375
Josep Elgueta, Generalized 2-vector spaces and general linear 2-groups Journal of Pure and Applied Algebra. ,vol. 212, pp. 2069- 2091 ,(2008) , 10.1016/J.JPAA.2007.12.010
John C. Baez, Higher-Dimensional Algebra II. 2-Hilbert Spaces☆ Advances in Mathematics. ,vol. 127, pp. 125- 189 ,(1997) , 10.1006/AIMA.1997.1617
Aaron D. Lauda, FROBENIUS ALGEBRAS AND AMBIDEXTROUS ADJUNCTIONS Theory and Applications of Categories [electronic only]. ,vol. 16, pp. 84- 122 ,(2006)