In algebraic topology, the Bousfield class of, say, a
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
''X'' is the set of all (say) spectra ''Y'' whose
smash product
In topology, a branch of mathematics, the smash product of two pointed spaces (i.e. topological spaces with distinguished basepoints) (''X,'' ''x''0) and (''Y'', ''y''0) is the quotient of the product space ''X'' × ''Y'' under the ide ...
with ''X'' is zero:
. Two objects are Bousfield equivalent if their Bousfield classes are the same.
The notion applies to
module spectra and in that case one usually qualifies a ring spectrum over which the smash product is taken.
See also
*
Bousfield localization In category theory, a branch of mathematics, a (left) Bousfield localization of a model category replaces the model structure with another model structure with the same cofibrations but with more weak equivalences.
Bousfield localization is named ...
External links
Ncatlab.org
References
{{topology-stub
Topology