## Category Theory For Beginners - 5 [entire topic moved to new forum]

tsakanikasnickos on Saturday, November 07 2015, 12:22 PM
0

Let $$\mathcal{F} : \mathcal{C} \longrightarrow \mathcal{D}$$ be a functor between the categories $$\mathcal{C}$$ and $$\mathcal{D}$$. Show that $$\mathcal{F}$$ is an equivalence if $$\mathcal{F}$$ induces bijections on the morphism sets and, additionally, for every object $$\displaystyle D$$ in $$\mathcal{D}$$ there is an object $$\displaystyle C$$ in $$\mathcal{C}$$ such that $$\displaystyle \mathcal{F} \left( C \right) \cong D$$.

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