You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Jonas Frey (Jun 17 2023 at 03:08):Is there a term for a commutative square of sets and functions (or in a topos), such that the "pushout gap map", ie the canonical map out of the pushout of the initial half of the square, is injective (a mono)?
If nobody has any better idea I'll write "weak pushout", although in the spirit of "weak (co)limit = existence but not uniqueness of mediating map", this term should better be used for case where the injection admits a retraction, meaning that the domain is as inhabited as the codomain.
Jonas Frey (Jun 17 2023 at 03:26):Ahh, in Joyal/Moerdijk's "Algebraic Set Theory", they call a square where the pullback gap-map is an epi a "quasi-pullback", so I guess I can say "quasi-pushout" by analogy.
Jonas Frey (Jun 17 2023 at 03:30):So the axiom of choice implies that quasi-pullback = weak pullback in Set, but weak pushout is a stronger condition than quasi-pushout.