finite limit and finite product and equalizer
1. Proposition
Let \(\mathcal{C}\) be a category.
TFAE:
- \(\mathcal{C}\) has all finite limits
- \(\mathcal{C}\) has equalizers and finite products
2. Proof
2.1. 1) \(\implies\) 2)
definitions
2.2. 2) \(\implies\) 1)
product and equalizer imply existence of a limit
finite union of finite sets as finite set (for other functor)