  The notion of semi-unital semi-monoidal category was defined a couple of
years ago using the so called "Takahashi tensor product" and so far, the only
example of it in the literature is complex. In this paper, we use the recently
defined "multiplicative tensor product of matrix factorizations" to give a
simple example of this a notion. In fact, if $MF(1)$ denotes the category of
matrix factorizations of the constant power series $1$, we define the concept
of one-step connected category and prove that there is a one-step connected
subcategory of $(MF(1),\widetilde{\otimes})$ which is semi-unital
semi-monoidal. We also define the concept of right pseudo-monoidal category
which generalizes the notion of monoidal category and we prove that
$(MF(1),\widetilde{\otimes})$ is an example of this concept.
