Suspension functor

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Template:Self-functor on topospaces

Definition

The suspension functor S is a functor from the category of topological spaces with continuous maps to itself, defined as follows:

  • It sends each topological space X to its suspension SX
  • Given a continuous map f:X \to Y, the induced map Sf:SX \to SY is the map naturally induced by quotienting out from the map X \times I \to Y \times I given by f \times id.

Iteration

The iteration of the suspension functor n times is equivalent to taking the join with a (n-1)-sphere.