标题： 论Diers的谱理论I：稳定函子和右多重伴随 显示英文标题

标题： On Diers theory of Spectrum I : Stable functors and right multi-adjoints

摘要： 迪尔斯发展了一种右多伴随函子的一般理论，导致了谱的纯范畴论、点集构造。 多普遍性质的情况返回一组规范解，而不是唯一的一个。 在右多伴随的情况下，每个对象都部署了一个规范锥体，共同承担伴随关系单位的角色。 第一部分围绕多伴随理论展开，并回顾或精确定义了后来在几何目的中将要用到的结果。 我们还研究了局部伴随的较弱概念，证明了与局部伴随相关的贝克-谢瓦莱条件，并证明了与稳定函子概念的等价性。 我们还回顾了与自由积完成的联系，并描述了多伴随情况下涉及的分解方面。 可及的右多伴随与局部有限多重表示范畴之间的关系也重新进行了探讨。 显示英文摘要

摘要： Diers developed a general theory of right multi-adjoint functors leading to a purely categorical, point-set construction of spectra. Situations of multiversal properties return sets of canonical solutions rather than a unique one. In the case of a right multi-adjoint, each object deploys a canonical cone of local units jointly assuming the role of the unit of an adjunction. This first part revolves around the theory of multi-adjoint and recalls or precises results that will be used later on for geometric purpose. We also study the weaker notion of local adjoint, proving Beck-Chevalley conditions relating local adjunctions and the equivalence with the notion of stable functor. We also recall the link with the free-product completion, and describe factorization aspects involved in a situation of multi-adjunction. The relation between accessible right multi-adjoints and locally finitely multipresentable categories is also revisited.