  A simplicial analogy of Chen's iterated integral was introduced in another
paper. However, its properties were hardly investigated in the paper. In
particular, no mention is made of whether it coincides with Chen's iterated
integral as a special case. In this paper, we answer this question. This paper
consists of two main parts. One of them is the research of elementary
properties of simplicial iterated integral. In particular, we describe a
relationship between iterated integral and homotopy pullback. The other one is
a comparison of Chen's iterated integral and simplicial iterated integral. At
the end of this paper, we observe Chen's theorem and Hain's theorem which
connects rational homotopy groups and (co)homologies of a smooth manifold, and
give an infinity-categorical viewpoint.
