The author generalizes the theory of polynomials from locally Cartesian closed categories (see [N. Gambino and J. Kock, Math. Proc. Camb. Philos. Soc. 154, No. 1, 153–192 (2013; Zbl 1278.18013)]) to the category with pullbacks. Moreover, the 2-categorical analog of the theory of polynomials is given.