Proposition 4.4. Assuming that:

• $C$ a category

Then

• (i) If $C$ has equalisers and all small products (including empty product), then $C$ has all small limits.
• (ii) If $C$ has equalisers and all finite products (including empty product), then $C$ has all finite limits.
• (iii) If $C$ has pullbacks and a terminal object, then $C$ has all finite limits.