From 536e8ba4d4d8ccc8c3d89a628d150277e17e656a Mon Sep 17 00:00:00 2001 From: Nathaniel Wesley Filardo Date: Wed, 6 Nov 2013 11:22:39 -0500 Subject: [PATCH] Fix typos --- adjoints-diag.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/adjoints-diag.tex b/adjoints-diag.tex index e57097a..8ce4dc7 100644 --- a/adjoints-diag.tex +++ b/adjoints-diag.tex @@ -145,8 +145,8 @@ Looking at this the other way, we have, in $\mathcal{C}$, X + X \ar[r]^(.75){\epsilon_X} & X \\ Y_1 + Y_2 \ar[u]^{f'_1 + f'_2} \ar[ur]_{f} } \] -Then if we take $\eta_X = [id,id]$ we can define $f' = (f \circ i_1) + (f -\circ i_2)$. This is unique and $\eta_X$ is natural by inspection. +Then if we take $\epsilon_X = [id,id]$ we can define $f' = (f \circ i_1) + (f +\circ i_2)$. This is unique and $\epsilon_X$ is natural by inspection. \section{Right Adjoint} \subsection{Unit} @@ -195,8 +195,8 @@ Here the counit diagram takes place in $\mathcal{C}^2$: (Y,Y) \ar[u]^{(f',f')} \ar[ur]_{(f_1,f_2)} } \] -Take $\eta_X = (\pi_1, \pi_2)$, then $f' = \ang{f_1, f_2}$. Uniqueness of -$f'$ is immediate. Naturality of $\eta_X$ is immediate from the action of +Take $\epsilon_X = (\pi_1, \pi_2)$, then $f' = \ang{f_1, f_2}$. Uniqueness of +$f'$ is immediate. Naturality of $\epsilon_X$ is immediate from the action of $\Delta\Pi$ on arrows: \[ \xymatrix{ (A \times B, A \times B) \ar[r] \ar[d]^{\Delta \Pi f} & (A, B) \ar[d]^{f} \\ -- 2.50.1