62 citations · 126 across the 28 of their papers we have counts for
10 papers · 1 filter
The Frobenius equivalence and Beck-Chevalley condition for Algebraic Weak Factorisation Systems
Wijnand van Woerkom, Benno van den Berg
If a locally cartesian closed category carries a weak factorisation system, then the left maps are stable under pullback along right maps if and only if the right maps are closed u…
Arrow algebras
Benno van den Berg, Marcus Briet
In this paper we introduce arrow algebras, simple algebraic structures which induce elementary toposes through the tripos-to-topos construction. This includes localic toposes as we…
Effective Kan fibrations in simplicial sets
Benno van den Berg, Eric Faber
We introduce the notion of an effective Kan fibration, a new mathematical structure that can be used to study simplicial homotopy theory. Our main motivation is to make simplicial…
Path categories and propositional identity types
Benno van den Berg
Connections between homotopy theory and type theory have recently attracted a lot of attention, with Voevodsky's univalent foundations and the interpretation of Martin-Lof's identi…
Exact completion of path categories and algebraic set theory -- Part I: Exact completion of path categories
Benno van den Berg, Ieke Moerdijk
We introduce the notion of a "category with path objects", as a slight strengthening of Kenneth Brown's classic notion of a "category of fibrant objects". We develop the basic prop…
Univalent completion
Benno van den Berg, Ieke Moerdijk
We review the concept of a univalent fibration and show by elementary means that every Kan fibration in simplicial sets can be embedded in a univalent Kan fibration.
Extending obstructions to noncommutative functorial spectra
Benno van den Berg, Chris Heunen
Any functor from the category of C*-algebras to the category of locales that assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on algebras of nxn-matrices…
W-types in Homotopy Type Theory
Benno van den Berg, Ieke Moerdijk
We will give a detailed account of why the simplicial sets model of the univalence axiom due to Voevodsky also models W-types. In addition, we will discuss W-types in categories of…
The Herbrand Topos
Benno van den Berg
We define a new topos, the Herbrand topos, inspired by the modified realizability topos and our earlier work on Herbrand realizability. We also introduce the category of Herbrand a…
Noncommutativity as a colimit
Benno van den Berg, Chris Heunen
Every partial algebra is the colimit of its total subalgebras. We prove this result for partial Boolean algebras (including orthomodular lattices) and the new notion of partial C*-…