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.
Tim Hosgood (May 03 2021 at 12:09):this coming thursday at 5pm UTC, as per usual!
Contractibility as uniqueness (Emily Riehl)
What does it mean for something to exist uniquely? Classically, to say that a set A has a unique element means that there is an element x of A and any other element y of A equals x. When this assertion is applied to a space A, instead of a mere set, and interpreted in a continuous fashion, it encodes the statement that the space A is contractible, i.e., that A is continuously deformable to a point. This talk will explore this notion of contractibility as uniqueness and its role in generalizing from ordinary categories to infinite-dimensional categories.
Tim Hosgood (May 03 2021 at 12:09):Zoom: https://topos-institute.zoom.us/j/5344862882?pwd=Znh3UlUrek41T3RLQXJVRVNkM3Ewdz09
YouTube: https://youtu.be/VdxdQiucJe8
Tim Hosgood (May 06 2021 at 16:43):starting in 15 minutes!
John Baez (May 06 2021 at 16:45):I think I was visiting MIT around 1992 when I went into the new grad student offices and saw someone - Charles Rezk? - sitting there, and he said "I realized that when people say something is unique it means there's a contractible space of choices of that thing."
John Baez (May 06 2021 at 16:49):James Dolan used to like to talk about "the generalized "the"": we're allowed to talk about "the" thing with some properties when given two things and with those properties, they are equivalent, and given two equivalences then they are equivalent, and given two equivalences they are equivalent, and so on ad infinitum.
John Baez (May 06 2021 at 16:50):But this is just a statement of contractibility, phrased in the language of globular -categories.