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UID:pretalx-qtcat-2026-VSBM8C@pretalx.c3voc.de
DTSTART;TZID=CET:20260814T103000
DTEND;TZID=CET:20260814T110000
DESCRIPTION:Each algebraic theory has some free algebras. Which algebraic t
 heories have the property that all their algebras are free? It turns out t
 hat it is not hard to state precisely which theories have this property\; 
 proving that they are the only ones is a much more difficult task. Proofs 
 were given in the 1970s in the language of logic by Steven Givant[1]\, and
  in the 2010s in the language of classical universal algebra by Keith A. K
 earnes\, Emil W. Kiss\, and Ágnes Szendrei[2]. Tom Leinster and I investi
 gated this result from a category theoretic point of view[3]: I will talk 
 about the theories in question\, highlighting some of their interesting pr
 operties.\n\nI will also spend some time asking what it might mean for us 
 to live in a world where everyone is free\, and in particular\, how we mig
 ht get there.\n\n[1] Steven Givant. Universal Horn classes categorical or 
 free in power. *Annals of Mathematical Logic*\, 15(1):1–53\, 1978.\n[2] 
 Keith A. Kearnes\, Emil W. Kiss\, and Ágnes Szendrei. Varieties whose fin
 itely generated members are free. *Algebra Universalis*\, 79\, 2018.\n[3] 
 Maia Woolf. *Algebraic theories all of whose algebras are free*. MScR Thes
 is\, University of Edinburgh\, 2025.
DTSTAMP:20260812T202111Z
LOCATION:R. 221
SUMMARY:Worlds where all are free - Maia Woolf (she/her)
URL:https://pretalx.c3voc.de/qtcat-2026/talk/VSBM8C/
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