arXiv Open Access 2022

What is an internal groupoid?

Nelson Martins-Ferreira
Lihat Sumber

Abstrak

An answer to the question investigated in this paper brings a new characterization of internal groupoids such that: (a) it holds even when finite limits are not assumed to exist; (b) it is a full subcategory of the category of involutive-2-links, that is, a category whose objects are morphisms equipped with a pair of interlinked involutions. This result highlights the fact that even thought internal groupoids are internal categories equipped with an involution, they can equivalently be seen as tri-graphs with an involution. Moreover, the structure of a tri-graph with an involution can be further contracted into a simpler structure consisting of one morphism with two interlinked involutions. This approach highly contrasts with the one where groupoids are seen as reflexive graphs on which a multiplicative structure is defined with inverses.

Topik & Kata Kunci

Penulis (1)

N

Nelson Martins-Ferreira

Format Sitasi

Martins-Ferreira, N. (2022). What is an internal groupoid?. https://arxiv.org/abs/2211.12531

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2022
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓