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Aspects of predicative algebraic set theory I: Exact Completion
 Ann. Pure Appl. Logic
"... This is the first in a series of three papers on Algebraic Set Theory. Its main purpose is to lay the necessary groundwork for the next two parts, one on ..."
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This is the first in a series of three papers on Algebraic Set Theory. Its main purpose is to lay the necessary groundwork for the next two parts, one on
A unified approach to algebraic set theory
 the proceedings of the Logic Colloquium 2006, arXiv:0710.3066
, 2007
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Abstract Nonwellfounded trees in categories
"... nonwellfounded sets, as well as nonterminating processes or infinite data structures. Categorically, they arise as final coalgebras for polynomial endofunctors, which we call Mtypes. We derive existence results for Mtypes in locally cartesian closed pretoposes with a natural numbers object, usi ..."
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nonwellfounded sets, as well as nonterminating processes or infinite data structures. Categorically, they arise as final coalgebras for polynomial endofunctors, which we call Mtypes. We derive existence results for Mtypes in locally cartesian closed pretoposes with a natural numbers object, using their internal logic. These are then used to prove stability of such categories with Mtypes under various topostheoretic constructions; namely, slicing, formation of coalgebras (for a cartesian comonad), and sheaves for an internal site. 1
WTYPES IN HOMOTOPY TYPE THEORY
"... The following full text is a preprint version which may differ from the publisher's version. For additional information about this publication click this link. ..."
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The following full text is a preprint version which may differ from the publisher's version. For additional information about this publication click this link.