17 citations · 67 across the 15 of their papers we have counts for
7 papers · 1 filter
Symmetric 2-rigs: coexponentiability and cartesian closure
Mathieu Anel, Marcelo Fiore, Nicola Gambino
We study coexponentiability in the context of the cocartesian 2-category RIG of symmetric 2-rigs, symmetric strong monoidal cocontinuous functors, and symmetric monoidal natural tr…
Left-exact Localizations of -Topoi III: The Acyclic Product
Mathieu Anel, Georg Biedermann, Eric Finster +1
We define a commutative monoid structure on the poset of left-exact localizations of a higher topos, that we call the acyclic product. Our approach is anchored in a structural anal…
Left-exact Localizations of -Topoi II: Grothendieck Topologies
Mathieu Anel, Georg Biedermann, Eric Finster +1
We revisit the work of Toën--Vezzosi and Lurie on Grothendieck topologies, using the new tools of acyclic classes and congruences. We introduce a notion of extended Grothendieck to…
The category of -finite spaces
Mathieu Anel
We show that the category of truncated spaces with finite homotopy invariants (\=/finite spaces) has many of the features expected of an elementary \oo topos. It should be thoug…
Left-exact Localizations of -Topoi I: Higher Sheaves
Mathieu Anel, Georg Biedermann, Eric Finster +1
We are developing tools for working with arbitrary left-exact localizations of -topoi. We introduce a notion of higher sheaf with respect to an arbitrary set of maps in…
Small object arguments, plus-construction, and left-exact localizations
Mathieu Anel, Chaitanya Leena Subramaniam
We present a variant of the small object argument, inspired by Kelly, better suited to construct unique factorisation systems. Our main result is to compare it to the plus-construc…