If someone cooked on Shabbos, we generally make a distinction between whether it was intentional (food is forbidden) and unintentional (food is permitted). However, regarding the laws of שהייה we are stricter. The rabbis said that even if it’s done unintentionally, the food is forbidden to eat. This was a second decree because ppl were doing שהייה intentionally and claiming it was unintentional.

Eggs are an example of מצתמק ויפה and cannot have שהייה even if they are fully cooked (like the rabanan)

Beis Hillel permits “chazara” to a fire on Shabbos that is גרוף וקטום. The gemara adds that the food should be kept in ones hands and not placed on the floor. (Placing on a peg or on a couch is a safek in the gemara)

There are two version regarding the variable of דעת regarding chazara. In the first, stricter opinion, in addition to the food being kept in ones hands, there also must be דעת להחזיר. In the second more lenient opinion, it is permissible to do chazara if either it is still in ones hands OR there was דעת להחזיר even if it is currently on the ground.

If one switched the contents of the pot to another pot, there is a safek in the gemara if chazara is permissible.

All of what we’ve discussed so far was with a כירה- a rectangular shaped stove top that fits two pots. Regarding a תנור- an old oven with a tiny hole on top, since the heat concentration is so much stronger, it is always assur to do שהייה- even if it fueled with weak fuel, like straw. It is even assur to place food close to that תנור.

For a כופח- a Square stovetop that fits one pot and is hotter than a Kirah but not as hot as a tanur, it depends on its fuel. If it is fueled by straw, then שהייה is permitted jsut like a kirah. If it is fueled with wood, then שהייה is assur jsut like a tanur.