
TL;DR
This paper introduces an abstract framework for projective lines over fields using first-order structures and groupoids, leading to a stack of projective lines with a natural notion of bundle and projectivity.
Contribution
It formalizes the concept of projective lines via first-order structures and groupoids, providing a new categorical perspective and a stack-based approach.
Findings
Defines an abstract projective line as a set with a first-order structure
Introduces projectivities as structure-preserving bijections
Develops a stack of bundles of projective lines
Abstract
We describe a notion of (abstract) projective line over a field as a set equipped with a certain first order structure, and a projectivity between projective lines as a bijection preserving this structure. The structure in question is that of a groupoid, with certain properties. This leads to a natural notion of bundle of projective lines, forming a stack.
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Taxonomy
TopicsMathematics and Applications · graph theory and CDMA systems · Advanced Theoretical and Applied Studies in Material Sciences and Geometry
