Elementary Category Theory - 1
-
- Community Team
- Posts: 314
- Joined: Tue Nov 10, 2015 9:25 pm
Elementary Category Theory - 1
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 and only 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 \( \displaystyle \mathcal{F} \left( C \right) \cong D \).
Create an account or sign in to join the discussion
You need to be a member in order to post a reply
Create an account
Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute
Sign in
Who is online
Users browsing this forum: No registered users and 0 guests