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Leonard Guetta
memoire
Commits
ccfd5294
Commit
ccfd5294
authored
Oct 29, 2020
by
Leonard Guetta
Browse files
edited some typos. Should look at log -2
parent
439a60a7
Changes
2
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homtheo.tex
View file @
ccfd5294
...
...
@@ -206,7 +206,7 @@ we shall use in the sequel.
\end{notation}
\begin{definition}
An
\emph
{
op
\nbd
{}
prederivator
}
is a (strict)
$
2
$
\nbd
{}
functor
\[
\sD
:
\CCat
^{
op
}
\to
\CCAT
.
\]
\[
\sD
:
\CCat
^{
\
op
}
\to
\CCAT
.
\]
More explicitly, an op
\nbd
{}
prederivator consists of the data of:
\begin{itemize}
[label=-]
\item
a big category
$
\sD
(
A
)
$
for every small category
$
A
$
,
...
...
@@ -271,7 +271,7 @@ we shall use in the sequel.
transformations between them. The correspondence
$
A
\mapsto
\C
(
A
)
$
is
$
2
$
\nbd
{}
functorial in an obvious sense and thus defines an op
\nbd
{}
prederivator
\begin{align*}
\C
:
\CCat
^{
op
}
&
\to
\CCAT
\\
\C
:
\CCat
^{
\
op
}
&
\to
\CCAT
\\
A
&
\mapsto
\C
(A)
\end{align*}
which we call the op
\nbd
{}
prederivator
\emph
{
represented by
$
\C
$}
. For
$
u : A
\to
...
...
@@ -322,7 +322,7 @@ We now turn to the most important way of obtaining op\nbd{}prederivators.
\]
Altogether, this defines an op
\nbd
{}
prederivator
\begin{align*}
\Ho
^{
\W
}
(
\C
) :
\CCat
^{
op
}
&
\to
\CCAT\\
\Ho
^{
\W
}
(
\C
) :
\CCat
^{
\
op
}
&
\to
\CCAT\\
A
&
\mapsto
\ho
(
\C
(A)),
\end{align*}
which we call the
\emph
{
homotopy op
\nbd
{}
prederivator of
$
(
\C
,
\W
)
$}
. When there is
...
...
main.pdf
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ccfd5294
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