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counit-unit_adjunction [2016/01/03 15:13] nikolaj |
counit-unit_adjunction [2016/01/03 15:17] nikolaj |
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| $\beta$ in $1_{\bf D}\cong GF$ | $\beta$ in $1_{\bf D}\cong GF$ | ||
| - | In the case of an adjunction, only the unit $\eta_{GX}$ (or $F(\eta_Y)$) can be inverted, but the nice thing is that the inverse is already something known, namely the other nat | + | In the case of an adjunction, only the unit arrows $\eta_{GX}$ (i.e. the units on the image of $G$) and the $F$-images of $\eta$ (i.e. $F(\eta_Y)$) can be inverted, but the nice thing is that the inverse is already something known, namely the other natural transformation |
| $\varepsilon_{FY}\circ F(\eta_Y)=1_{FY}$ | $\varepsilon_{FY}\circ F(\eta_Y)=1_{FY}$ | ||
