We define the analytic spectrum of a rig category $(A,\oplus,\otimes)$, and equip it with a sheaf of categories of rational functions. If the category is additive, we define a sheaf of categories of analytic functions. We relate this construction to Berkovich's analytic spaces, to Durov's generalized schemes and to Haran's F-schemes. We use these relations to define analytic versions of Arakelov compactifications of affine arithmetic varieties.
Keywords: Rig categories, global analytic geometry, generalized rings, Arakelov compactifications
2010 MSC: 18D10, 14G22, 14G25, 11G35, 18C15
Theory and Applications of Categories, Vol. 29, 2014, No. 6, pp 188-197.