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(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.

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Definition of an attractor of a stack under an action of $G_{m}$

For an algebraic space $Z$ with the action of multiplicative group scheme $G_{m}$ one can define the attractor space $Z^{+}$ as the functor which sends a scheme $S$ to the set $Map(S \times A^{1},Z)^{ …