Correspondence -- the class of all correspondences

Description

A correspondence $I$ from from an AbstractVariety $X$ (the source of $I$) to another AbstractVariety $Y$ (the target of $I$) consists of two functions $I_*$ and $I^*$, which take cycles on $X$ to cycles on $Y$ and vice-versa, respectively. In general these functions are not ring maps or even module maps. See Correspondence ^* and Correspondence _* for more info.

Unlike an IncidenceCorrespondence, a general Correspondence need not have an intermediate variety.

Types of Correspondence :

IncidenceCorrespondence -- the class of all incidence correspondences

Functions and methods returning an object of class Correspondence :

Correspondence * Correspondence -- composition of correspondences
transpose(Correspondence) -- reverse the direction of a correspondence

Methods that use an object of class Correspondence :

Correspondence ^* -- pullback along a correspondence
Correspondence _* -- pushforward along a correspondence
source(Correspondence) -- the source of a correspondence
target(Correspondence) -- the target of a correspondence

For the programmer

The object Correspondence is a type, with ancestor classes MutableHashTable < HashTable < Thing.