From the 2 of 5 linked papers with an AI index.
5 papers
Operadic 2-rigs
M. Anel, M. Fiore, N. Gambino
The paper introduces operadic 2‑rigs and proves that the bicategory of operads and bimodules embeds fully into the bicategory of symmetric 2‑rigs, showing this sub‑bicategory is th…
Symmetric 2-rigs: coexponentiability and cartesian closure
Mathieu Anel, Marcelo Fiore, Nicola Gambino
The paper investigates which symmetric 2‑rig structures can be coexponentiated, showing they are exactly deformation retracts of presheaf categories, and uses this to describe cart…
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 monoidal localizations from tidy maps
Mathieu Anel, Georg Biedermann, Eric Finster +1
We put Goodwillie's calculus of functors and Weiss' orthogonal calculus in a unified framework. We do so in two ways. On the one hand, the relevant categories are all symmetric mon…
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 thou…