  In this short note, we provide a calculation of the Euler characteristic of a
finite homotopy colimit of finite cell complexes, which depends only on the
Euler characteristics of each space and resembles Mobius inversion. Versions of
the result are known when the colimit is indexed by a finite category, but the
behavior is more uniform when we index by finite quasicategories instead. The
formula simultaneously generalizes the additive formula for Euler
characteristic of a homotopy pushout and the multiplicative formula for Euler
characteristic of a fiber bundle.
