nLab
Sheaves in Geometry and Logic

This entry is about the book

• Sauders MacLane, Ieke Moerdijk, Sheaves in Geometry and Logic.

For more information on “sheaves in geometry and logic” see for instance

• sheaf and topos theory

• sheaf

• topos

For a similar link list with considerable overlap see

• Categories and Sheaves

Categorical Preliminaries

I Categories of Functors

• presheaf

II Sheaves of Sets

• category of open subsets

• sheaf

• global section/constant sheaf

III Grothendieck Topologies and Sheaves

• presheaf

• Grothendieck topology

  • site

  • sheaf

    • sheafification

    • direct image

    • inverse image

    • restriction and extension of sheaves

    • stalk

  • category of sheaves

• Grothendieck topos

IV First Properties of Elementary Topoi

• subobject classifier

  • subobject

• topos

  • Grothendieck topos

  • well-pointed topos

  • Boolean topos

  • pretopos

  • universe in a topos

• point of a topos

• fundamental group of a topos

• dependent product

• infinity-topos

V Basic Constructions of Topoi

• Lawvere-Tierney topology

• sheafification in a Lawvere-Tierney topos

VI Topoi and Logic

• logic

• foundations and logic

  • internal logic

    • intuitionistic logic

    • classical logic

    • paraconsistent logic

    • coherent logic

• Boolean algebra

• Heyting algebra

VII Geometric Morphisms

• geometric morphism

  • geometric embedding

  • point of a topos

    • stalk

VIII Classifying Topoi

• classifying topos

IX Localic Topoi

• locale

• localic topos

Geometric Logic and Classifying Topoi

• classifying topos

Appendix: Sites for Topoi

category: reference