Last Updated：2025/12/31
Sentence
Moreover,
f∗
admits
both
a
left
adjoint
f_!
and
a
right
adjoint
f_∗,
given
by
left
and
right
Kan
extension
along
the
map
SingY→SingX,
respectively.
Note
that
this
is
left
and
right
Kan
extension
in
the
∞-categorical
sense,
which
amounts
to
homotopy
left
and
right
Kan
extension
on
the
level
of
simplicial
categories
or
model
categories.
Quizzes for review
Moreover, f∗ admits both a left adjoint f_! and a right adjoint f_∗, given by left and right Kan extension along the map SingY→SingX, respectively. Note that this is left and right Kan extension in the ∞-categorical sense, which amounts to homotopy left and right Kan extension on the level of simplicial categories or model categories.
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