nLab mapping space - contents

internal hom/mapping space

General abstract

• hom-set, hom-object, internal hom, exponential object, derived hom-space

• loop space object, free loop space object, derived loop space

Topology

• mapping space (compact-open topology)

• topology of mapping spaces

• evaluation fibration of mapping spaces

• loop space, free loop space

  • free loop space of a classifying space

Simplicial homotopy theory

• simplicial mapping complex

• inertia groupoid

Differential topology

• differential topology of mapping spaces

  • C-k topology

• manifold structure of mapping spaces

  • tangent spaces of mapping spaces

• smooth loop space

Stable homotopy theory

• mapping spectrum

Geometric homotopy theory

• mapping stack

• inertia stack

• free loop stack

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