论文标题
组合代数的内部作业
The Internal Operads of Combinatory Algebras
论文作者
论文摘要
我们认为，运营提供了一个通用框架，用于处理多项式和组合代数的结合性，包括经典的$ \ Mathbf {sk} $ - 代数，线性$ \ mathbf {bci} $ - 代数 - 代数 - planar $ \ m m mathbf {bibraire as bras as bras as bbr as as bras as as as \ _） $ \ mathbf {bc^\ pm i} $ - 代数。我们表明，每个扩展的组合代数都会产生一个规范的封闭式奥尔塔尔，我们将其称为组合代数的内部作业。内部的作业结构从封闭的作战界到了伸展组合代数。作为副产品，我们为上述组合代数类得出扩展性公理。
We argue that operads provide a general framework for dealing with polynomials and combinatory completeness of combinatory algebras, including the classical $\mathbf{SK}$-algebras, linear $\mathbf{BCI}$-algebras, planar $\mathbf{BI}(\_)^\bullet$-algebras as well as the braided $\mathbf{BC^\pm I}$-algebras. We show that every extensional combinatory algebra gives rise to a canonical closed operad, which we shall call the internal operad of the combinatory algebra. The internal operad construction gives a left adjoint to the forgetful functor from closed operads to extensional combinatory algebras. As a by-product, we derive extensionality axioms for the classes of combinatory algebras mentioned above.
