arXiv Open Access 2022

The Internal Operads of Combinatory Algebras

Masahito Hasegawa

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Abstrak

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.

Topik & Kata Kunci

cs.LO

Penulis (1)

Masahito Hasegawa

Format Sitasi

APA MLA BibTeX

Hasegawa, M. (2022). The Internal Operads of Combinatory Algebras. https://arxiv.org/abs/2211.11118

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓