In
category theory
Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...
, a branch of mathematics, a stable model category is a
pointed model category
In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called ' weak equivalences', 'fibrations' and ' cofibrations' satisfying certain axioms relating them. These abstract ...
in which the suspension functor is an equivalence of the homotopy category with itself.
The prototypical examples are the category of
spectra 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 F ...
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
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