附加词的抽象与应用
Abstraction and Application in Adjunction
摘要：
集合论中的可理解性和可拓性的假设是基于一个反演原理，该原理将集合论的抽象和具有成员的性质联系起来。一个完全类似的反演原理将函数的抽象和应用与lambda演算的假设中的一个参数联系起来。这样的反演原理也出现在两个伴随的情况下，涉及一个carnival闭范畴和它的多项式扩张。这两个概念的组合产生了连接乘积和幂运算的附加物，即合取和蕴涵。
英文摘要：
The postulates of comprehension and extensionality in set theory are based on an inversion principle connecting set-theoretic abstraction and the property of having a member. An exactly analogous inversion principle connects functional abstraction and application to an argument in the postulates of the lambda calculus. Such an inversion principle arises also in two adjoint situations involving a cartesian closed category and its polynomial extension. Composing these two adjunctions, which stem from the deduction theorem of logic, produces the adjunction connecting product and exponentiation, i.e. conjunction and implication.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
