nLab fractured (infinity,1)-topos

Idea

A kind of local generalization of cohesive $\infty$-toposes.

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Examples

• Apparently condensed mathematics takes place in fractured $\infty$-topoi, see at condensed local contractibility.

References

• Jacob Lurie, Fractured $\infty$-Topoi, Chapter 20 in: Spectral Algebraic Geometry

following

• David Carchedi, Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity Topoi, Memoirs of the American Mathematical Society 264 1282 (2020) [doi:10.1090/memo/1282, arXiv:1312.2204]

The example of condensed local contractibility:

• Qi Zhu, Fractured Structure on Condensed Anima, MSc thesis (2023) [pdf, pdf]

exposition:

• Qi Zhu, Fractured structure on condensed spaces, talk notes (2023) [pdf, pdf]

• Nima Rasekh, What is a topological structure?, talk notes (April 2023) [pdf, pdf]