Fibrations as Eilenberg-Moore algebras

2013/12/05 by Anders Kock, Kock, Anders
Mathematics · #18C15 #18D30 #Category Theory (math.CT) #FOS: Mathematics #math.CT #msc:18C15 #msc:18D30

paper · pdf · doi:10.48550/arxiv.1312.1608

arxiv created 2013/12/05 · arxiv updated 2013/12/06

Abstract

We give an elementary exposition of some fundamental facts about fibered (or rather opfibered) categories, in terms of monads and 2-categories. The account avoids any mention of category-valued functors and pseudofunctors.

Related

• Fibrations of algebras
• Grothendieck's theory of fibred categories for monoids
• Synthetic fibered (∞,1)-category theory
• Fibred 2-categories and bicategories
• Geometric constructions preserve fibrations