nLab grouplike geometric morphism

1. Idea

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2. Definition

A geometric morphism $p:\mathcal{E} \to\mathcal{S}$ (, or the $\mathcal{S}$-topos $\mathcal{E}$ it corresponds to) is called grouplike if for every $\mathcal{S}$-topos $q:\mathcal{F} \to\mathcal{S}$ the category of 1-cells from $q$ to $p$ in the 2-category $\mathbf{Top}/\mathcal{S}$ of $\mathcal{S}$-toposes is a groupoid.

3. Properties

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4. Related entries

• local geometric morphism

• totally connected geometric morphism

5. Reference

• Peter Johnstone, Sketches of an Elephant vol.2 , Oxford UP 2002. (C3.6.9; p.703, 710)