Timeline for Ultrafilters as a double dual

6 events

when toggle format	what		by	license	comment
Mar 12, 2019 at 17:26	history	rollback	Will Sawin		Rollback to Revision 2
Mar 12, 2019 at 17:24	history	edited	Will Sawin	CC BY-SA 4.0	added 1 character in body
Mar 9, 2019 at 20:45	history	edited	Qiaochu Yuan	CC BY-SA 4.0	deleted 1 character in body
Mar 9, 2019 at 20:42	comment	added	Qiaochu Yuan		(Then the right adjoint is the "second dual," although it's a bit trickier to describe.)
Mar 9, 2019 at 20:39	comment	added	Qiaochu Yuan		There is a kind of "double dual" in this story, by the way: one way to describe the codensity monad of $F : C \to D$, if $C$ is essentially small and $D$ has small limits, is that it's the monad associated to the adjunction between $D$ and $[C, \text{Set}]^{op}$ whose left adjoint sends $d \in D$ to the functor $\text{Hom}(d, F(-)) : C \to \text{Set}$. When $F$ is the inclusion of finite sets into sets this is a disguised form of $\beta X$ and when $F$ is the inclusion of finite-dimensional vector spaces into vector spaces this is a disguised form of taking the dual.
Mar 8, 2019 at 8:05	history	answered	Qiaochu Yuan	CC BY-SA 4.0