Editing Alexandroff extension (section)

=== As a functor ===
The Alexandroff extension can be viewed as a [[functor]] from the [[category of topological spaces]] with proper continuous maps as morphisms to the category whose objects are continuous maps <math>c\colon X \rightarrow Y</math> and for which the morphisms from <math>c_1\colon X_1 \rightarrow Y_1</math> to <math>c_2\colon X_2 \rightarrow Y_2</math> are pairs of continuous maps <math>f_X\colon X_1 \rightarrow X_2, \ f_Y\colon  
Y_1 \rightarrow Y_2</math> such that <math>f_Y \circ c_1 = c_2 \circ f_X</math>.  In particular, homeomorphic spaces have isomorphic Alexandroff extensions.