There are some variants on the coefficient ring/field of the local system. The simplest case is the trivial local system, in which case we simply delete the $\Hom$ factor. Other popular choices have parallel transport in $\mathbb{Q}^{*},\mathbb{R}^{*},\mathbb{C}^{*}$, or the units in the Novikov ring.⁶³⁶³ 63 The $U(1)$-local systems are popular in the physics literature, but appear rarely in Floer theory. Different choices could in principle lead to slightly different versions of the derived Fukaya category. The smaller the coefficient ring/field, the more stringent is the notion of derived isomorphism of objects. For the purpose of extending the Solomon functional (cf. section 20) to be real valued, we require all coefficients to be at least contained in $\mathbb{R}$, so we will usually work simultaneously with $\mathbb{R}$, $\mathbb{Q}$ and $\mathbb{Z}$ local systems. On the other hand, it is claimed in [81, Remark 4.5] that in the exact setting the immersed Fukaya algebras can be defined over the integers. The specific advantage of working over integers, as discussed in the main text, is primarily that the bordism current $\mathcal{C}$ between Lagrangians is then an integral current, rather than $\mathbb{R}$-linear combinations of integral currents.