edge maps. Similarly, if for every p < 0, then there is a sequence of epimorphisms (also called the edge maps): . The transgression is a partially-defined map (more precisely, a map from a subobject to a quotient) given as a composition , the first and last maps being the inverses of the edge maps. Cohomological spectral sequences For a spectral sequence of cohomological type, the analogous statements hold. If for every q < 0, then there is a sequence of epimorphisms . And if for every p < 0, then there is a sequence of monomorphisms: . The transgression is a not necessarily well-defined map: induced by . Application Determining these maps are fundamental for computing many differentials in the Serre spectral sequence. For instance the transgression map determines the differential for the homological spectral spectral sequence, hence on the Serre spectral sequence for a fibration gives the map . Further examples Some notable spectral sequences are: Topology and geometry Atiyah–Hirzebruch spectral sequence of an extraordinary cohomology theory Bar spectral sequence for the homology of the classifying space of a group. Bockstein spectral sequence relating the homology with mod p coefficients and the homology reduced mod p. Cartan–Leray spectral sequence converging to the homology of a quotient space. Eilenberg–Moore spectral sequence for the singular cohomology of the pullback of a fibration Serre spectral sequence of a fibration Homotopy theory Adams spectral sequence in stable homotopy theory Adams–Novikov spectral sequence, a generalization to extraordinary cohomology theories. Barratt spectral sequence converging to the homotopy of the initial space of a cofibration. Bousfield–Kan spectral sequence converging to the homotopy colimit of a functor. Chromatic spectral sequence for calculating the initial terms of the Adams–Novikov spectral sequence. Cobar spectral sequence EHP spectral sequence converging to stable homotopy groups of spheres Federer spectral sequence converging to homotopy groups of a function space. Homotopy fixed point spectral sequence Hurewicz spectral sequence for calculating the homology of a space from its homotopy. Miller spectral sequence converging to the mod p stable homology of a space. Milnor spectral sequence is another name for the bar spectral sequence. Moore spectral sequence is another name for the bar spectral sequence. Quillen spectral sequence for calculating the homotopy of a simplicial group. Rothenberg–Steenrod spectral sequence is another name for the bar spectral sequence. van Kampen spectral sequence for calculating the homotopy of a wedge of spaces. Algebra Čech-to-derived functor spectral