In
category theory, a branch of mathematics, a stable model category is a
pointed model category in which the suspension functor is an equivalence of the homotopy category with itself.
The prototypical examples are the category of
spectra
Spectra may refer to:
* The plural of spectrum, conditions or values that vary over a continuum, especially the colours of visible light
* ''Spectra'' (journal), of the Museum Computer Network (MCN)
* The plural of spectrum (topology), an object ...
in the
stable homotopy theory
In mathematics, stable homotopy theory is the part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the ...
and the category of chain complex of ''R''-modules. On the other hand, the category of pointed topological spaces and the category of pointed simplicial sets are not stable model categories.
Any stable model category is equivalent to a category of
presheaves of spectra.
References
* Mark Hovey: ''Model Categories'', 1999, .
Category theory
{{categorytheory-stub