SpaceSuch functorsXis sent to a sequence of Vector SpacesH_{0}(X),H_{1}(X),H_{2}(X), ...

- can be manipulated as functions (just better),
- are insensitive to "deformations",
- reduce many questions to algebra

the "wheighted sum" of the indices of the singularities of the field

is equal to

the "Euler characteristic" ofXdim H_{0}(X) - dimH_{1}(X) + dimH_{2}(X) - ...

Bjørn Ian Dundas