论文标题
关于DIERS频谱理论I：稳定的函子和正确的多连接
On Diers theory of Spectrum I : Stable functors and right multi-adjoints
论文作者
论文摘要
Diers开发了一种右多跳功能子的一般理论，导致纯粹的分类点集谱图。多元属性的情况返回规范解决方案的集合，而不是独特的解决方案。在正确的多个配合的情况下，每个对象都会部署本地单元的规范锥，共同承担相邻单位的作用。第一部分围绕多偶会的理论，并回忆或精确的结果，这些结果将在后面用于几何目的。我们还研究了局部伴随的较弱概念，证明了贝克 - 切瓦利条件与局部辅助关系以及与稳定函子的概念有关。我们还回想起与五自由行完成的联系，并描述多次裁缝情况所涉及的分解方面。还重新审视了可访问的右多个接合队与本地有限多重多种类别之间的关系。
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.
