categories: Re: Looking for adjoints

[Michael Batanin <mbatanin@ics.mq.edu.au>]

This is just a small correction to Michael Barr message. The Kan's
Ex^{\infty} is not a left adjoint to the inclusion of Kan simplicial sets
into simplicial sets. In the original paper by Kan "On c.s.s. complexes"
there is no mention about it being adjoint.
Yet, the following  is true

  Kan(Ex^{\infty}X,Y) is homotopy equivalent to Ssets(X,Y).

So it is some sort of homotopy adjunction.


Michael Batanin.

>on 2/4/01 9:16 PM, Michael Barr at barr@barrs.org wrote:


> The earliest that was labelled such was Kan's Ex^\infty, which was a left
> adjoint to the inclusion of (what are now called) Kan simplicial sets into
> simplicial sets.
>