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marcbezem
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Merge branch 'master' of github.com:UniMath/SymmetryBook
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congp.tex

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@@ -206,17 +206,20 @@ \section{The pullback}
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\begin{xca}
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Prove that if $f:\Hom(H,G)$ and $f':\Hom(H',G)$ are homomorphisms,
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then the pointed version of \cref{xca:univpropofpullback} induces an equivalence
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$$
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\Hom(K,H)\times_{\Hom(K,G)}\Hom(K,H')\simeq \Hom(K,H\times_GH')
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$$
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for all groups $K$ and an equivalence
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then the pointed version of \cref{xca:univpropofpullback} induces an
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equivalence
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\[
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\Hom(K,H)\times_{\Hom(K,G)}\Hom(K,H')\simeq \Hom(K,H\times_GH')
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\]
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for all groups $K$ and an equivalence%
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\stepcounter{footnote}\footnotetext{%
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Hint: set $A\defequi \Sc$, $B\defequi \BH$, $C\defequi \BH'$ and $D\defequi \BG$.}%
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\addtocounter{footnote}{-1}
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\[
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\USymH \times_{\USymG} \USymH'
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\simeq (\shape_{H\times_GH'}=\shape_{H\times_GH'}).\text{\footnotemark}
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\]
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Elevate the last equivalence to a statement about abstract groups.\footnotetext{%
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Hint: set $A\defequi \Sc$, $B\defequi \BH$, $C\defequi \BH'$ and $D\defequi \BG$.}
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Elevate the last equivalence to a statement about abstract groups.
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\end{xca}
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\begin{remark}

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