SomethingRelatedToEmbedding 2006-12-24 07:32:23 2007-06-10 23:51:00 Definition embedding % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here From the most general -categorical- point of view, an embedding between two objects $A,B$ in a category $\cal{C}$ is a $\cal{C}$-morphism $f\colon A\to B$ which is injective. So, for example, the adjectives topological, algebraic or geometrical should be used, respectively, when we talk of embeddings between topological spaces, algebraic structures or geometries.