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Lawvere–Tierney sheaves in Algebraic Set Theory

  • S. Awodey (a1), N. Gambino (a2), P. L. Lumsdaine (a3) and M. A. Warren (a4)

We present a solution to the problem of denning a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

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  • ISSN: 0022-4812
  • EISSN: 1943-5886
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