

Homotopical Algebra

Those who have been studying algebraic topology often
realize that some operations on spaces and continous
maps look similar to algebraic constructions. For
example,
localizations of spaces
,
homotopy (co)limits
, and
calculus of functors
.
We collect such “algebraic operations on
spaces” in this page. The term
“homotopical algebra” is used in this
sense, although it is the title of Quillen’s
book
[
Qui67
]
in which he introduced the notion of
closed model category
. The term “homotopical algebra” is often
used for theory of model categories. Nowadays, the
notion of model categories is very popular, I guess no
confusion arises if the term “homotopical
algebra” is used in the above sense.


