Brief Notes on Sheaves Theory

TL;DR

This paper provides a concise overview of sheaves theory, highlighting their differences from presheaves, bundles, and manifolds, and clarifies their distinct mathematical structures and original purposes.

Contribution

It offers a brief, comparative explanation of sheaves and related concepts, emphasizing their unique roles and foundational differences in mathematics.

Findings

Clarifies differences between sheaves, presheaves, and bundles

Highlights the purpose of sheaves in mathematical structures

Provides insights into singularities and manifolds

Abstract

Essentials of sheaves are briefly presented, followed by related comments on presheaves, bundles, manifolds and singularities, aiming to point to their differences not only in their different formal mathematical structures, but also in the very purposes for which they were introduced in the first place.