\begin{equation*}
\DeclareMathOperator\Coim{Coim}
\DeclareMathOperator\Coker{Coker}
\DeclareMathOperator\Ext{Ext}
\DeclareMathOperator\Hom{Hom}
\DeclareMathOperator\Im{Im}
\DeclareMathOperator\Ker{Ker}
\DeclareMathOperator\Mor{Mor}
\DeclareMathOperator\Ob{Ob}
\DeclareMathOperator\Sh{Sh}
\DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}}
\DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}}
\DeclareMathOperator\Spec{Spec}
\newcommand\colim{\mathop{\mathrm{colim}}\nolimits}
\newcommand\lim{\mathop{\mathrm{lim}}\nolimits}
\newcommand\Qcoh{\mathit{Qcoh}}
\newcommand\Sch{\mathit{Sch}}
\newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}}
\newcommand\Cohstack{\mathcal{C}\!\mathit{oh}}
\newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}}
\newcommand\Quotfunctor{\mathrm{Quot}}
\newcommand\Hilbfunctor{\mathrm{Hilb}}
\newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}}
\newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}}
\newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}}
\newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits}
\newcommand\Picardstack{\mathcal{P}\!\mathit{ic}}
\newcommand\Picardfunctor{\mathrm{Pic}}
\newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}}
\end{equation*}
70 Groupoids in Algebraic Spaces
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Section 70.1: Introduction
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Section 70.2: Conventions
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Section 70.3: Notation
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Section 70.4: Equivalence relations
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Section 70.5: Group algebraic spaces
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Section 70.6: Properties of group algebraic spaces
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Section 70.7: Examples of group algebraic spaces
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Example 70.7.1: Multiplicative group algebraic space
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Example 70.7.2: Roots of unity as a group algebraic space
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Example 70.7.3: Additive group algebraic space
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Example 70.7.4: General linear group algebraic space
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Example 70.7.5
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Example 70.7.6: Constant group algebraic space
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Section 70.8: Actions of group algebraic spaces
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Section 70.9: Principal homogeneous spaces
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Section 70.10: Equivariant quasi-coherent sheaves
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Section 70.11: Groupoids in algebraic spaces
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Section 70.12: Quasi-coherent sheaves on groupoids
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Section 70.13: Crystals in quasi-coherent sheaves
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Section 70.14: Groupoids and group spaces
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Section 70.15: The stabilizer group algebraic space
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Section 70.16: Restricting groupoids
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Section 70.17: Invariant subspaces
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Section 70.18: Quotient sheaves
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Section 70.19: Quotient stacks
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Section 70.20: Functoriality of quotient stacks
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Section 70.21: The 2-cartesian square of a quotient stack
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Section 70.22: The 2-coequalizer property of a quotient stack
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Section 70.23: Explicit description of quotient stacks
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Section 70.24: Restriction and quotient stacks
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Section 70.25: Inertia and quotient stacks
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Section 70.26: Gerbes and quotient stacks
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Section 70.27: Quotient stacks and change of big site
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Section 70.28: Separation conditions