Corollary 7.3 (05UQ) · ScalingStacks

[05UQ]

Corollary 7.3. If $W$ is a complete Segal space (resp. a Segal space) and $X$ is any simplicial space, then $W^{X}$ is a complete Segal space (resp. a Segal space).

[05UR]

Proof. This is a direct consequence of the compatibility of these model category structures with the cartesian closure, since any object is cofibrant in either of these model category structures. ∎