Editing Covering space (section)

=== Definitions ===
==== Category of coverings ====
Let <math>X</math> be a topological space. The objects of the [[Category theory|category]] '''<math>\boldsymbol{Cov(X)}</math>''' are the coverings <math>p:E \rightarrow X</math> of <math>X</math> and the [[Morphism (category theory)|morphisms]] between two coverings <math>p:E \rightarrow X</math> and <math>q:F\rightarrow X</math> are continuous maps <math>f:E \rightarrow F</math>, such that the diagram 
[[File:Kommutierendes_Diagramm_Cov.png|center|frameless]]
commutes.

==== G-Set ====
Let <math>G</math> be a [[topological group]]. The [[Category theory|category]] <math>\boldsymbol{G-Set}</math> is the category of sets which are [[G-set|G-sets]]. The morphisms are [[Group action#Morphisms and isomorphisms between G-sets|G-maps]] <math>\phi:X \rightarrow Y</math> between G-sets. They satisfy the condition <math>\phi(gx)=g \, \phi(x)</math> for every <math>g \in G</math>.