Readme.txt The following files contains Coq proofs for the fact that the setoids form a locally cartesian closed pretopos and in particular a locally cartesian closed category. Categories are here defined without assuming equality on objects (so called e-categories). PropasTypesUtf8Notation.v This file contains notations in UTF8 for propositions as types notions at the Set level. Author: Olov Wilander 2012. PropasTypesBasics_mod.v A collection of basic definition and lemmas for Propositions as types at the Set level. Author: Olov Wilander 2012 SwedishSetoids_mod.v This contains definitions and results relating to setoids where the equivalence relation has truth values in Set (and not in Prop as in the standard Coq library). The binary sum, binary product and the coequalizer constructions for the category of setoids are established. Author: Olov Wilander 2012. families_of_setoids_and_LCCC.v Contains a proof that the setoids form a locally cartesian closed category, using Pi- and Sigma-constructions for families of setoids. Author: Erik Palmgren 2012.