Is the property of a geometric morphism being both connected and locally connected (in the sense of Part C of the Elephant) stable under pullbacks? I know local connectedness is, I am not sure about connectedness. Thanks!
2026-03-30 10:10:11.1774865411
Question on connected and locally connected geometric morphisms.
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Theorem 3.3.15 in Part C says that connected and locally connected geometric morphisms are stable under pullback (along bounded geometric morphisms), and Example 3.3.17 says that connected geometric morphisms need not be stable under pullback (along bounded geometric morphisms).