An incidence correspondence $I$ is a correspondence from an AbstractVariety $X$ (the source of $I$) to another AbstractVariety $Y$ (the target of $I$) which is mediated by a third AbstractVariety $Z$, together with AbstractVarietyMaps $f:Z\rightarrow X$ and $g:Z\rightarrow Y$.
Given a cycle $x$ on $X$, the pushforward of $x$ along $I$ is $$I_* x = g_* f^* x,$$ and similarly for bundles on $X$. Likewise, if $y$ is a cycle on $Y$, the pullback of $y$ along $I$ is $$I^* y = f_* g^* y,$$ and similarly for bundles on $Y$. See Correspondence ^* and Correspondence _* for more info.
The tuple $(Z,f,g)$ can be accessed via the intermediates command.
The object IncidenceCorrespondence is a type, with ancestor classes Correspondence < MutableHashTable < HashTable < Thing.