Category Theory
Zulip Server
Archive

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.

Stream: deprecated: id my structure

Topic: unbalanced isomorphism through an adjunction

Josselin Poiret (Oct 03 2022 at 19:12):

Let $L \dashv R : C \rightarrow D$ be an adjunction and $f : RX \rightarrow Y, g : LY \rightarrow X$ morphisms. Now, instead of asking the mate of $g$ to be a two-sided inverse for $f$, is there a name for $f \circ R g \circ \eta \simeq id$ (left-sided inverse of the mate) and $g \circ L f \simeq \varepsilon$?

For those who saw it, I deleted my previous post since there were quite some errors and some simplifications could be done.

Josselin Poiret (Oct 03 2022 at 19:19):

well, seems I could have pondered that 3 minutes longer. It's actually equivalent to being a 2 sided inverse, by using the triangle identities.