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two dimensional sheaf theory

Ross Street has written the articles

  • Two dimensional sheaf theory, J. Pure Appl. Algebra 23 (1982) 251-270
  • Characterization of bicategories of stacks, in: Category theory (Gummersbach 1981) Springer Lecture Notes in Mathematics 962, 1982, pp 282-291 transcript

where the stacks are considered on a 2-site. A 2-site is a 2-category with a Grothendieck 2-topology (compare Grothendieck topology), which is in turn defined in terms of 2-sieves (compare sieve). There is a Giraud-type theorem proved in this context. In a later article there were some errata mentioned.

This should be related to the ”\infty-dimensional sheaf theory” described at (infinity,1)-category of (infinity,1)-sheaves, somehow. Compare also derived stack.

Zoran: Could one define (,1)(\infty,1)-sieves somehow as subobjects (in quasi-category sense) of representables in enriched quasi-category setup ?

So if \infty-stacks are really (,1)(\infty,1)-sheaves, and stacks are really (2,1)(2,1)-sheaves, then these are the real 22-sheaves, that is (2,2)(2,2)-sheaves? (with notation following that of (n,r)(n,r)-category). —Toby

category: sheaf theory

Revised on March 6, 2013 19:54:24 by Zoran Škoda (161.53.130.104)