In A Primer on Galois Connections, the authors define a Galois connection thus (definition 1, p. 104).
Consider posets $\mathcal{P} = \langle P, \leq\rangle$ and $\mathcal{Q} = \langle Q,\sqsubseteq\rangle$. If $P\overset{\pi_*}{\rightarrow} Q$ and $Q\overset{\pi^*}{\rightarrow} P$ are functions such that for all $p \in P$ and all $q \in Q$ $$ p \leq \pi^*(q)\quad \text{iff}\quad \pi_*(p)\sqsubseteq q $$ then the quadruple $\pi = \langle\mathcal{P},\pi_*,\pi^*,\mathcal{Q}\rangle$ is called a Galois connection.
They follow this definition by a listing of various kinds of Galois connections. One of these kinds is as follows.
We say that $\pi$ is [...] an interior (respectively, closure) connection if $\pi_*$ (respectively, $\pi^*$) is an inclusion.
What does 'inclusion' mean in this context? Does it mean inclusion map? In other words, is a Galois connection called interior if $P \subseteq Q$ and $\pi_*$ is the identity map?
ERNÉ M, KOSLOWSKI J, MELTON A, STRECKER G. A Primer on Galois Connections. Ann N Y Acad Sci. 1993; 103-125. doi:10.1111/j.1749-6632.1993.tb52513.x.