Last Updated：2025/12/20
Sentence
A
model
category
is
called
pointed
if
the
initial
object
and
terminal
object
are
the
same.
The
homotopy
category
of
any
pointed
model
category
acquires
a
suspension
functor
denoted
by
𝛴.
It
turns
out
that
Ho(M)
is
a
pre-triangulated
category
in
a
natural
way[…].
When
the
suspension
is
an
equivalence,
M
is
called
a
stable
model
category,
and
in
this
case
Ho(M)
becomes
a
triangulated
category[…].
Quizzes for review
A model category is called pointed if the initial object and terminal object are the same. The homotopy category of any pointed model category acquires a suspension functor denoted by 𝛴. It turns out that Ho(M) is a pre-triangulated category in a natural way[…]. When the suspension is an equivalence, M is called a stable model category, and in this case Ho(M) becomes a triangulated category[…].
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