Quotient Stacks
CIMAT Centro de Investigación en Matemáticas, A.C. SOME RESULTS IN QUOTIENT STACKS TESIS Que para obtener el grado de Doctor en Ciencias con Orientación en Matemáticas Básicas Presenta Diego Alexander Acosta Álvarez Director de Tesis: Dr. Pedro Luis del Ángel Rodriguez Autorización de la versión nal Guanajuato, Gto, 27 de agosto de 2016 Dedication To my parents Patricia Álvarez Villada Héctor Jaime Acosta Vélez i Acknowledgements I must acknowledge a lot of people and institutions who significantly contributed to the re- alization of this work and myself. First, and foremost to my advisor, Pedro Luis, without whose support, patience and understanding I would have been lost in half way. My family, who have accompanied me throughout my life, their affection and support have been funda- mental in the path. CIMAT, an incredible research center full of lovely people who welcomed me and gave me the opportunity to achieve this academic goal. An special recognition to my teachers, classmates and the staff of the School Services department. CONACyT, magnifi- cent institution that gave me sufficient financial support to devote my efforts exclusively to my studies. Last, but not least to México, Mexican are the kindest people I have known in my life, during all these years I felt at home. I keep in my heart a very special place for this country. ¡Viva México! iii Contents Introduction1 1 Fibred categories5 1.1 2-categories................................... 6 1.2 Categories over a category ........................... 15 1.3 Fibred categories ................................ 21 1.4 Fibred category associated to a functor..................... 40 1.5 Fibred categories in groupoids ........................
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