\begin{tikzcd}
B \arrow[r, "\mathrm{P}"] \arrow[rr, bend right=35, "\pi"'] & X \arrow[r, "\pi_{0}"] & (\mathrm{Ens})
\end{tikzcd}

\begin{tikzcd}
Z \arrow[r, "i"] \arrow[dr, "p"'] & C \arrow[r, "\overline{\mathrm{P}}"] \arrow[d, "q"] & X \\
 & B \arrow[u, dashed, "\sigma"'] &
\end{tikzcd}

\begin{tikzcd}
C_{c_{\infty}} \arrow[r, "u'_{i*}"] & C_{b_{i}}
\end{tikzcd}

\begin{tikzcd}
E \arrow[r, "u"] \arrow[d] & E' \arrow[d] \\
\mathfrak{P}^{*}(E) \arrow[r] & \mathfrak{P}^{*}(E')
\end{tikzcd}

\begin{tikzcd}
B \arrow[r, "\pi"] \arrow[rr, bend right=35, "\widetilde{\pi}"'] & (\mathrm{Ens}) \arrow[r, "\mathfrak{P}^{*}"] & (\mathrm{Ord})
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
c \arrow[r, "\mathrm{cocart}"] \arrow[rr, bend left=30, "v_{i}"] & u_{\infty*}(c) = c_{\infty} \arrow[r, "w_{i}"] & c_{i} = (b_{i},E_{i}) \\
b \arrow[r, "u_{\infty}"] \arrow[rr, bend right=30, "u_{i}"'] & b_{\infty} = \varprojlim b_{i} \arrow[r, "u'_{i}"] & b_{i}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
Z \arrow[r, "i"] \arrow[d, "p"'] \arrow[rr, bend left=30, "\mathrm{cocart}"] & C \arrow[r, "\varphi"] \arrow[dl, "q"] & Z^{\wedge} \arrow[d, "p_{!}"] \\
B \arrow[rr, "c_{B}"'] & & B^{\wedge}
\end{tikzcd}

\begin{tikzcd}
(\widetilde{\Delta}^{\,\circ})^{\wedge} \arrow[r] & X^{\wedge}
\end{tikzcd}

\begin{tikzcd}
Y^{\wedge} \arrow[r, "f"] & Z^{\wedge}
\end{tikzcd}

\begin{tikzcd}
B \arrow[r, "\pi"] & (\mathrm{Ens}) \arrow[r, "\mathfrak{P}^{*}"] & (\mathrm{Ord})
\end{tikzcd}

\begin{tikzcd}
B \arrow[r, "\pi"] & (\mathrm{Ens}) \arrow[r, "\mathfrak{P}^{*}"] & (\mathrm{Ord}) \arrow[r, "\mathrm{can.}"] & (\mathrm{Cat})
\end{tikzcd}

\begin{tikzcd}
e \arrow[r, bend left=25, "u"] \arrow[r, bend right=25, "v"'] & x \arrow[r, bend left=25, "\alpha"] \arrow[r, bend right=25, "\beta"'] & a
\end{tikzcd}

\begin{tikzcd}
z \arrow[r] & x \arrow[r, bend left=25] \arrow[r, bend right=25] & y
\end{tikzcd}

\begin{tikzcd}
& a_{j} \\
a \arrow[ur] \arrow[dr] & \\
& a_{i}
\end{tikzcd}

\begin{tikzcd}
x_{1} \arrow[r, bend left=25] \arrow[r, bend right=25] & x_{0}
\end{tikzcd}

\begin{tikzcd}
x \arrow[r] \arrow[d] & y \arrow[d] \\
H_{x} \arrow[r] \arrow[d, "\mathrm{iso}?"] & H_{y} \\
\lbrack x \rbrack &
\end{tikzcd}

\begin{tikzcd}
e \arrow[r, bend left=25, "u"] \arrow[r, bend right=25, "v"'] & x
\end{tikzcd}

\begin{tikzcd}
x \arrow[r, "f"] & y \arrow[r, "g"] & z \\
& e \arrow[ul, "u"] \arrow[u, "v"] \arrow[ur, "w"'] &
\end{tikzcd}

\begin{tikzcd}
x \arrow[r, "f"] & y \arrow[r, "g"] & z \\
 & e \arrow[ul, "u"'] \arrow[u, "v"] \arrow[ur, "w"]
\end{tikzcd}

\begin{tikzcd}
e \arrow[r, "\lambda", bend left=25] \arrow[r, "\mu"', bend right=25] & \xi = a\sigma
\end{tikzcd}

\begin{tikzcd}
 & e \arrow[dr, "\lambda"] \\
\eta \arrow[ur, "\lambda'"] \arrow[dr, "\mu'"'] & & \xi \\
 & e \arrow[ur, "\mu"']
\end{tikzcd}

\begin{tikzcd}
& b \arrow[dr, "u"] & \\
e \arrow[ur, "p_b"] \arrow[rr, "p"'] & & a
\end{tikzcd}

\begin{tikzcd}
& b \arrow[dr, "u", bend left=15] \arrow[dr, "v"', bend right=15] & \\
e_a \arrow[ur, bend left=15] \arrow[ur, bend right=15]
    \arrow[rr, "p_a"'] & & a
\end{tikzcd}

\begin{tikzcd}
e \arrow[r, "p"] \arrow[d, bend right=25] & a \\
e \arrow[u, bend right=25] \arrow[ur] &
\end{tikzcd}

\begin{tikzcd}
& b \arrow[dr, "u"] & \\
e \arrow[ur, "p_u"] \arrow[rr] & & q
\end{tikzcd}

\begin{tikzcd}
& q & \\
e \arrow[ur] \arrow[dr, "p_v"'] & & \\
& b \arrow[uu, "v"'] &
\end{tikzcd}

\begin{tikzcd}
G \arrow[r, "u"] & F \arrow[r, "\varphi"] & E
\end{tikzcd}

\begin{tikzcd}
F_s \arrow[r] & F_{s'}
\end{tikzcd}

\begin{tikzcd}
s & s' \arrow[l]
\end{tikzcd}

\begin{tikzcd}
X \arrow[r] & \mathrm{Groupoïdes}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
& Z \arrow[d] & \Psi \arrow[l, hook'] \arrow[d] \\
e \arrow[r] \arrow[ur] & X' & X \arrow[l, hook']
\end{tikzcd}

\begin{tikzcd}
S \arrow[d] \\
e \backslash X \arrow[d] \\
X
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
A_1 \arrow[r] \arrow[dr] & B \\
A_2 \arrow[r] & c
\end{tikzcd}

\begin{tikzcd}
x \arrow[r, bend left=14] \arrow[r, bend right=14] & a
\end{tikzcd}

\begin{tikzcd}
\mathrm{Hom}(a,x)\times E \arrow[d] \\
\mathrm{Hom}(a,a)\times E
\end{tikzcd}

\begin{tikzcd}
& b \\
a \arrow[ru] \arrow[r, "u"] \arrow[rd] & x \\
& c
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
& Z = e\backslash X \sim S^{1} \arrow[ld, "\text{asph.}"'] \arrow[rd, "\text{asph.}"] & \\
e \arrow[rd] & & X \arrow[ld] \\
& X' \sim S^{2} &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
& e\backslash X = Z \arrow[ld, "\text{asph.}"'] \arrow[rd] & \\
e \arrow[rd] & & e\backslash X \arrow[ld, "\text{asph.}"] \\
& X' &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
& (b_{0}\amalg c_{0})/\!/X_{0} \arrow[ld] \arrow[rd] & \\
b_{0}/\!/X_{0} \arrow[rd, "W\text{-cocart.}"'] & & c_{0}/\!/X_{0} \arrow[ld] \\
& T \arrow[ld] \arrow[rd] & \\
X_{0} = {}_{a}\backslash X \arrow[rd, hook, "W\text{-cocart.}"'] & & {}_{a}\backslash X = X_{0} \arrow[ld] \\
& e\backslash X = \tilde X \arrow[ld] \arrow[rd, "\text{coét.}"] & \\
e \arrow[rd, "W\text{-cocart.\,!}"'] & & X \arrow[ld] \\
& X' &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
& X_{0} \arrow[ld] & \\
X_{1} \arrow[rd] & & X_{2} \arrow[ld] \arrow[lu] \\
& X_{3} &
\end{tikzcd}

\begin{tikzcd}
a \arrow[r, bend left=14] \arrow[r, bend right=14] & b
\end{tikzcd}

\begin{tikzcd}
X \arrow[r, "u\in W"] \arrow[d, "i\in W_{S}''"'] & Y \arrow[d, "j\in W_{S}''"] \\
\bar X \arrow[r, "\bar u\in W"'] & \bar Y
\end{tikzcd}

\begin{tikzcd}
X \arrow[r, "W_{S}''"] \arrow[d] & \mathcal{G}(X) \arrow[ld] \\
S &
\end{tikzcd}

\begin{tikzcd}
X' \arrow[r] \arrow[d] & X \arrow[d] \\
S' \arrow[r, "w"] & S
\end{tikzcd}

\begin{tikzcd}
X_{/F} \arrow[r, hook, "i"] & X' \arrow[r] & e
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
& T \arrow[ld] \arrow[rd] & \\
\beta/\!/\tilde X \arrow[rd, "\text{cocart.}"'] & & \gamma/\!/\tilde X \arrow[ld] \\
& \tilde X \arrow[ld, "X\ \text{asph.}"'] \arrow[rd] & \\
X \arrow[rd, "W\text{-cocart.}"'] & & e \arrow[ld] \\
& X' &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
\alpha \arrow[r, "u_{1}'"] \arrow[rd, "u_{1}''"] & B \\
\beta \arrow[ru, "u_{2}'"] \arrow[r, "u_{2}''"'] & C
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
a \arrow[r, "u_{1}"] \arrow[rd, "w"'] & b \arrow[d] \\
& x
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
a \arrow[rd] & \\
& F \\
b \arrow[ru] &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
& a \arrow[rd] & \\
c \arrow[ru, dashed] \arrow[rd, dashed] & & F \\
& b \arrow[ru] &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
& \xi & \\
a \arrow[ru, "\lambda"] \arrow[rd, "\lambda'"'] & & b \arrow[lu, "\mu"'] \arrow[ld, "\mu'"] \\
& \xi' &
\end{tikzcd}

\begin{tikzcd}
\alpha \arrow[r, bend left=16, "u_{1}"] \arrow[r, bend right=16, "u_{2}"'] & b \arrow[r, "v"] & x
\end{tikzcd}

\begin{tikzcd}
a \arrow[r, bend left=16, "v"] \arrow[r, bend right=16, "w"'] & x
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
\alpha \arrow[r, "\tilde u"] & \tilde\xi \\
\beta \arrow[r, "\tilde w"'] & \tilde\xi
\end{tikzcd}

\begin{tikzcd}
S \arrow[r, hook, "\text{cocof.}"] \arrow[d] & Z \arrow[r, "\text{ou}"] \arrow[d] & e \arrow[d, no head] \\
X \arrow[r, hook] & X' \arrow[r, "\text{ou}"'] & e
\end{tikzcd}

\begin{tikzcd}
\alpha \arrow[r, bend left=16] \arrow[r, bend right=16] & \beta \arrow[r] & \gamma
\end{tikzcd}

\begin{tikzcd}
a \arrow[r, bend left=16] \arrow[r, bend right=16] & b \arrow[r] & c
\end{tikzcd}

\begin{tikzcd}
\alpha \arrow[r, bend left=16] \arrow[r, bend right=16] & \beta \arrow[r] & C
\end{tikzcd}

\begin{tikzcd}
X_{/\!/b} & \tilde X \arrow[l] & X_{/\!/a} \arrow[l, "\text{cocart.}"']
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
& \tilde\xi & \\
\tilde a \arrow[ru, "\tilde\lambda"] \arrow[rd, "\tilde\lambda'"'] & & \tilde b \arrow[lu, "\tilde\mu"'] \arrow[ld, "\tilde\mu'"] \\
& \tilde\xi' &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
\tilde a \arrow[r, "\tilde u"] & \tilde\xi \\
\tilde u' \arrow[r] & \tilde\xi'
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
& \xi \\
a \arrow[ru, "u"] \arrow[rd, "u'"'] & \\
& y
\end{tikzcd}

\begin{tikzcd}
D \arrow[r, "\text{cofinal}"] \arrow[d] & Z \arrow[r, "\text{ou}"] \arrow[d] & e \arrow[d, no head] \\
X \arrow[r, hook, "\text{cofinal}"'] & X' \arrow[r, "\text{ou}"'] & e
\end{tikzcd}

\begin{tikzcd}
a \arrow[r, bend left=14] \arrow[r, bend right=14] & b
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
& T = \tilde X_{/\!/(\tilde a,\tilde b)} \arrow[ld] \arrow[rd] & \\
\tilde X_{/\!/\tilde b} \arrow[rd, "W\text{-cocart.}"'] & & \tilde X_{/\!/\tilde a} \arrow[ld] \\
& \simeq \Sigma^{1}(T) \arrow[ld] \arrow[rd] & \\
\tilde X_{/\!/\tilde\xi} \arrow[rd, "W\text{-cocart.}"'] & & \tilde X_{/\!/\tilde\xi'} \arrow[ld] \\
& \tilde X \simeq \Sigma^{1}_{W}(T) \arrow[ld] \arrow[rd] & \\
X \arrow[rd] & & e \arrow[ld] \\
& X' &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & \tilde a \arrow[dr, dashed] & \\
\tilde x \arrow[ur, "v"] \arrow[dr, "w"'] & & \tilde c \\
 & \tilde b \arrow[ur, dashed] &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & a \\
x \arrow[ur, "v"] \arrow[dr, "w"'] & \\
 & b
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & a \\
x' \arrow[ur, "v"] \arrow[dr, "w"'] & \\
 & b
\end{tikzcd}