# SpectralSequencePageMap -- the type of all spectral sequence page maps

## Description

A (homological, or lower index) spectral sequence page map consists of:

1. A fixed integer $r \geq 0$, the page number;

2. A collection of homomorphisms $\{d^r_{p,q}: E^r_{p,q} \rightarrow E^r_{p-r,q+r-1}\}$ for $p,q \in \mathbb{Z}, r \geq 0$ such that $d^r_{p,q} d^r_{p+r,q-r+1} = 0$.

Alternatively a (cohomological, or upper index) spectral sequence page consists of:

1'. A fixed integer $r \geq 0$, the page number;

2'. A collection of homomorphisms $\{d_r^{p,q}: E_r^{p,q} \rightarrow E_r^{p+r,q-r+1}\}$ for $p,q \in \mathbb{Z}, r \geq 0$ such that $d_r^{p,q} d_r^{p-r,q+r-1} = 0$.

The type SpectralSequencePageMap is a data type for working with spectral sequences and the differentials on the pages of a spectral sequence.