\begin{tikzcd}
\widetilde{C} = F \arrow[r, "\widetilde{v}_{0}"] \arrow[d, hook] & \widetilde{C}' = F' \arrow[d, hook] \\
\widehat{C} \arrow[r, "\widehat{v}_{0}"] & \widehat{C}'
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\Pi(\widetilde{C}, F) \arrow[r, "{\Pi(\mathrm{id}_{\widetilde{C}}, v)_{*}}"] \arrow[d, "{\Pi(i_{C}, \mathrm{id}_{F})_{*}}"'] & \Pi(\widetilde{C}, F') \arrow[d, "{\Pi(i_{C}, \mathrm{id}_{F'})_{*}}"] \\
\Pi(\widehat{C}, F) \arrow[r, "{\Pi(\mathrm{id}_{\widehat{C}}, v)_{*}}"'] & \Pi(\widehat{C}, F')
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\prod_{i} \operatorname{Hom}_{\mathrm{top}}(X, E'_{i}) \arrow[r, hook, "\alpha"'] & \prod_{i} \operatorname{Hom}_{\mathrm{top}}(X, E_{i}) \\
& \operatorname{Hom}_{\mathrm{top}}(X, E) \arrow[u, "\beta"']
\end{tikzcd}

\begin{tikzcd}
\operatorname{Hom}(\widetilde{C}, E) \arrow[r, bend left=20, "\alpha"] & \operatorname{Hom}(C,E) \arrow[l, bend left=20, "\beta"]
\end{tikzcd}

\begin{tikzcd}
\operatorname{Hom}(C,E) \arrow[r, bend left=20, "\widehat{\beta}"] & \operatorname{Hom}'(\widehat{C}, E) \arrow[l, bend left=20, "\widehat{\alpha}"]
\end{tikzcd}

\begin{tikzcd}
(\mathrm{Esp}) \arrow[r, bend right=20, "\alpha"'] & (\text{Préord})
\arrow[l, bend right=20, "\beta"']
\end{tikzcd}

\begin{tikzcd}[column sep=large]
O_{X} \arrow[r, "{U \mapsto (U,V)}"] & O_{X} \times O_{Y}
\arrow[r, "{(U,V) \mapsto U \times V}"] & \underline{O}_{X \times Y} \\
O_{Y} \arrow[ur, "{V \mapsto (X,V)}"'] & &
\end{tikzcd}

\begin{tikzcd}
C^{1} \arrow[r] & C^{2} \arrow[r] & C^{3} \arrow[r] & C^{4}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
{[C^{0}]} \arrow[r] & C^{0} \times Z^{1} \arrow[d, bend right=20]
\arrow[d, bend left=20] & \\
& Z^{1} \arrow[r] & C^{1} \times Z^{2} \arrow[d, bend right=20]
\arrow[d, bend left=20] \\
& \operatorname{Aut}(0) \arrow[u] & 0 \to Z^{2}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
E_{\bullet} \arrow[d, bend right=20] \arrow[d, bend left=20] &
\Pi \times E \arrow[d, bend right=20] \arrow[d, bend left=20] & \Pi \arrow[d] \\
E_{1} \arrow[d, bend right=20] \arrow[d, bend left=20] & E \arrow[d] & 1 \\
E_{0} \arrow[d] & X & \\
X & &
\end{tikzcd}

\begin{tikzcd}[column sep=large]
\underline{\operatorname{End}}(\mathcal{G}) \otimes
\underline{\operatorname{End}}(\mathcal{E})
\arrow[r, "\varphi_{\mathcal{G},\mathcal{E}}"]
\arrow[d, "\lambda \otimes \underline{\operatorname{End}}(v)"'] &
\underline{\operatorname{End}}(\mathcal{G} \otimes \mathcal{E})
\arrow[d, "\underline{\operatorname{End}}(w)"] \\
\underline{\operatorname{End}}(\mathcal{G}) \otimes
\underline{\operatorname{End}}(\mathcal{E})
\arrow[r, "\varphi_{\mathcal{G},\mathcal{E}}"] &
\underline{\operatorname{End}}(\mathcal{G} \otimes \mathcal{E})
\end{tikzcd}

\begin{tikzcd}
T(C) \arrow[r, "T(u)"] \arrow[d, "\varphi^{T}_{C}"'] & T(C')
\arrow[d, "\varphi^{T}_{C'}"] \\
C^{I} \arrow[r, "u^{I}"'] & C'^{I}
\end{tikzcd}

\begin{tikzcd}
\mathrm{Ob}\,\Gamma^{T} \arrow[rr] & & \mathrm{Ob}\,\Gamma_{0}^{T} \\
& I \arrow[ul] \arrow[ur] &
\end{tikzcd}

\begin{tikzcd}
\underline{\mathrm{Mor}\,\mathrm{Top}}(X,Y) \arrow[r, hook, "\text{pl.\ fid.}"']
& \underline{\operatorname{Hom}}\,\underline{\mathrm{cat}}(X,Y)
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
& S' \arrow[dr, dashed] & \\
S \arrow[ur] \arrow[rr] & & R
\end{tikzcd}

\begin{tikzcd}[column sep=large, nodes={font=\scriptsize}]
\operatorname{Hom}_{\underrightarrow{\lambda}}(R, \mathbb{Z}) \arrow[r, "\text{fid.}"]
& \operatorname{Hom}_{\underrightarrow{\lambda}}(S', \mathbb{Z}) \arrow[r, hook, "\text{pl.\ fid.}"]
& \operatorname{Hom}_{\underrightarrow{\lambda}}(S, \mathbb{Z})
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
(\mathrm{Cat}_{\lambda'}) \arrow[r] & (\mathrm{Cat}_{\lambda}) \\
\mathrm{Cat} \supset \mathrm{cofib}(\mathrm{Cat}_{\lambda}) \arrow[r] \arrow[d]
& \mathrm{Cat} \supset \mathrm{cofib}(\mathrm{Cat}_{\lambda'}) \\
(\lambda\text{-types}) \arrow[r, dashed, "?"] \arrow[d]
& (\lambda'\text{-types}) \arrow[u] \\
(\mathrm{Cat}_{\lambda}) \arrow[r, dashed]
& (\mathrm{Cat}_{\lambda'}) \arrow[u]
\end{tikzcd}

\begin{tikzcd}[row sep=small]
C \arrow[r, hook] & (\check{C})^{\circ}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\operatorname{Hom}_{\lambda}(R, C) \arrow[r, hook, "\text{2-cart}"] \arrow[d, "\varphi_{C}"]
& \operatorname{Hom}_{\lambda}(R, \widehat{C}\,) \arrow[d, "\varphi_{\widehat{C}}"] \\
C^{I} \arrow[r, hook] & \widehat{C}^{\,I}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
T_{\lambda}(C) \arrow[r, hook] \arrow[d] & T_{\lambda}(C') \arrow[d] \\
C^{+} \arrow[r, hook] & C'^{+}
\end{tikzcd}

\begin{tikzcd}
\widehat{C}' \arrow[r, "u^{*}"] & \widehat{C}
\end{tikzcd}

\begin{tikzcd}[row sep=small]
T(C) \arrow[r] \arrow[d, "b^{T}_{C}"] & T(C') \arrow[d, "b^{T}_{C'}"] \\
C^{I} \arrow[r] & C'^{I}
\end{tikzcd}

\begin{tikzcd}[column sep=huge, row sep=small]
C \arrow[r, "f"] & C' \\
C & C' \arrow[l, dashed, "g"'] \\
C \arrow[r, dashed, "h"] & C'
\end{tikzcd}

\begin{tikzcd}[column sep=huge, row sep=small]
\widehat{C} \arrow[r, "f_{!}"] & \widehat{C}' \\
\widehat{C} & \widehat{C}' \arrow[l, "f^{*}"'] \\
\widehat{C} \arrow[r, "f_{*}"] & \widehat{C}'
\end{tikzcd}

\begin{tikzcd}[row sep=large]
(B_{G})_{/X} \arrow[r, "\varphi\ \approx"] \arrow[d, "j_{X}"]
& B_{H} \arrow[d, "B_{i}"] \\
B_{G} & B_{G}
\end{tikzcd}

\begin{tikzcd}[row sep=small]
E \arrow[r] & X \\
F \arrow[u] \arrow[r, dashed] & e_{E} \arrow[u, "\varepsilon"']
\end{tikzcd}