Editing Module homomorphism (section)

== Variant: additive relations ==
{{see also|binary relation}}
An '''additive relation''' <math>M \to N</math> from a module ''M'' to a module ''N'' is a submodule of <math>M \oplus N.</math><ref name=maclane/> In other words, it is a "[[many-valued function|many-valued]]" homomorphism defined on some submodule of ''M''. The inverse <math>f^{-1}</math> of ''f'' is the submodule <math>\{ (y, x) | (x, y) \in f \}</math>. Any additive relation ''f'' determines a homomorphism from a submodule of ''M'' to a quotient of ''N''
:<math>D(f) \to N/\{ y | (0, y) \in f \}</math>
where <math>D(f)</math> consists of all elements ''x'' in ''M'' such that (''x'', ''y'') belongs to ''f'' for some ''y'' in ''N''.

A [[Spectral sequence#Edge maps and transgressions|transgression]] that arises from a spectral sequence is an example of an additive relation.