Year: 2018
Type: preprint
Abstract: Two adjoint functors can be seen as generalisations of the two functions within a Galois connection. If instead the adjoints are not generalised from functions, but from relations, then analogously the object of study becomes a more general notion of an adjunction. A suitable method to express such functor-level relations is to consider functors into categories of families. This structure is then used to show that the central exactness structure in self-dual group theory, consisting of a chain of adjunctions, holds also for the category of sets when seen in this general form. EDIT: Please see the note about the empty set on page 4!
Source: arXiv (Cornell University)
Author: van Zyl, Phillip-Jan
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2887836968