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Exercise 38 - Chapter 3

Say where each morphism in \( \mathcal{F} \) is sent under the functor \(F\).

Example 3.30

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  • 1.
    edited June 11

    The compositions will both map to \(f . h\). $$ \begin{array}{c|c} \text{morphism }f & F~f \\\hline \text{id}_A' & \text{id}_A \\ \text{id}_B' & \text{id}_B \\ \text{id}_C' & \text{id}_C \\ \text{id}_D' & \text{id}_D \\ f' & f \\ g' & g \\ h' & h \\ i' & i \\ f' . h' & f . h \\ g' . i' & f . h \end{array} $$

    Comment Source:The compositions will both map to \\(f . h\\). $$ \begin{array}{c|c} \text{morphism }f & F~f \\\hline \text{id}_A' & \text{id}_A \\ \text{id}_B' & \text{id}_B \\ \text{id}_C' & \text{id}_C \\ \text{id}_D' & \text{id}_D \\ f' & f \\ g' & g \\ h' & h \\ i' & i \\ f' . h' & f . h \\ g' . i' & f . h \end{array} $$
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