arXiv:1808.01350math.CT
A Generalised Exactness Structure for Sets
Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.
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!
This is also true of QM (not just because of QM computational sciences). My MSc thesis has application to quantum mechanics. I wrote a short summary of the generalisation that I made here [1], which generalises what the Nijmegen group calls quotient comprehension chains to sets.…
mikorymView on HNParent context