Welcome to mathimatikoi.org forum; Enjoy your visit here.

Category Theory for beginners (5)

Categories
Post Reply
Tsakanikas Nickos
Community Team
Community Team
Articles: 0
Posts: 314
Joined: Tue Nov 10, 2015 8:25 pm

Category Theory for beginners (5)

#1

Post by Tsakanikas Nickos » Sat Jan 16, 2016 11:21 pm

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 \( \displaystyle \mathcal{F} \left( C \right) \cong D \).
Post Reply