Question in Derivation of Lie algebra

In Weinberg’s QFT Volume 1 Chapter2, he "derives" the Lie algebra from the Lie group as follows

[…] a connected Lie group […is a…] group of transformations ?($theta$) that are described by a finite set of real continuous parameters, say $?^a$, with each element of the group connected to the identity by a path within the group. The group multiplication law then takes the form
$$
T(bar{theta}) T(theta)=T(f(bar{theta}, theta)).tag{2.2.15}
$$
With $?^?(bar{theta},theta)$ a function of the $bar{?}’s$and $theta$‘s. Taking $theta^{a} = 0$ as the coordinates of the identity, we must have
$$
f^{a}(bar{theta}, 0)=f^{a}(0, theta)=theta^{a}.tag{2.2.16}
$$

Now I wonder whether it writes wrong here, as I think it should be
$$
f^{a}(0, theta)=theta^{a},f^{a}(bar{theta}, 0)=bar{theta}^{a}.
$$