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Tesi.log
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This is pdfTeX, Version 3.141592653-2.6-1.40.29 (TeX Live 2026/Arch Linux) (preloaded format=pdflatex 2026.4.6) 15 MAY 2026 19:11 This is pdfTeX, Version 3.141592653-2.6-1.40.29 (TeX Live 2026/Arch Linux) (preloaded format=pdflatex 2026.4.6) 15 MAY 2026 20:28
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@@ -875,7 +875,7 @@ exmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb></usr/share/texmf-dist/fonts
msfonts/cm/cmti12.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/symbol msfonts/cm/cmti12.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/symbol
s/msam10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10. s/msam10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.
pfb></usr/share/texmf-dist/fonts/type1/public/cm-super/sfrm1200.pfb> pfb></usr/share/texmf-dist/fonts/type1/public/cm-super/sfrm1200.pfb>
Output written on Tesi.pdf (21 pages, 323499 bytes). Output written on Tesi.pdf (21 pages, 323585 bytes).
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\end{tikzcd}\] \end{tikzcd}\]
where $F\cdot f: X \to \Gamma (FA)$ is the set function defined sending $x \in X$ into the global setion of $FA$ given by $F( f(x)) : 1_\mathcal{B} \to FA$ where $F\cdot f: X \to \Gamma (FA)$ is the set function defined sending $x \in X$ into the global setion of $FA$ given by $F( f(x)) : 1_\mathcal{B} \to FA$
\begin{proof} \begin{proof}
By lemma \ref{cover of cc is cc} $Cov(-)$ exentend to a class function from \textbf{biCC} to itself. Then notice that the action of $Cov(-)$ over arrows of \textbf{biCC} is well defined since the commutativity condition of the arrow is preserved under the action of $F$. Indeed By lemma \ref{cover of cc is cc} $Cov(-)$ exentend to a class function from \textbf{biCC} to itself. Then notice that the action of $Cov(-)$ over arrows of \textbf{biCC} is well defined since the commutativity condition of the arrow is preserved under the action of $F$. Indeed by definition of $F \cdot f$ and $F \cdot g$ we have:
\[ \[
Ff : (F \cdot g) \circ h = F(\Gamma k) \circ (F \cdot f)
\] \]
\end{proof} \end{proof}
\end{proposition} \end{proposition}