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Peter LeFanu Lumsdaine
Peter LeFanu Lumsdaine
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Theorem 2 in these notesthese notes[1] states that, roughly, that each Grothendieck topos can be built (using limits and colimits) from localic topoi. To what extent is that related to the theorem of Joyal and Tierney which states that each Grothendieck topos is equivalent to the topos of equivariant sheaves on a groupoid in the category of locales?

  1. Jacob Lurie, 2018, lecture notes from Math 278X Categorical Logic, https://www.math.ias.edu/~lurie/278x.html, Lecture 16 Enumerations

Theorem 2 in these notes states that, roughly, that each Grothendieck topos can be built (using limits and colimits) from localic topoi. To what extent is that related to the theorem of Joyal and Tierney which states that each Grothendieck topos is equivalent to the topos of equivariant sheaves on a groupoid in the category of locales?

Theorem 2 in these notes[1] states that, roughly, that each Grothendieck topos can be built (using limits and colimits) from localic topoi. To what extent is that related to the theorem of Joyal and Tierney which states that each Grothendieck topos is equivalent to the topos of equivariant sheaves on a groupoid in the category of locales?

  1. Jacob Lurie, 2018, lecture notes from Math 278X Categorical Logic, https://www.math.ias.edu/~lurie/278x.html, Lecture 16 Enumerations
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user477332
user477332
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Every Grothendieck topos can be built from localic topoi

Theorem 2 in these notes states that, roughly, that each Grothendieck topos can be built (using limits and colimits) from localic topoi. To what extent is that related to the theorem of Joyal and Tierney which states that each Grothendieck topos is equivalent to the topos of equivariant sheaves on a groupoid in the category of locales?