Pigeon

Hi we are looking for a bit of advice about a new friend we have. We thought it was a homing pigeon, but it has no leg band. We know nothing about pigeons, but this one is super friendly and will happily land on your hand and sit on your shoulder. It followed my husband home three days ago and it won't leave our garden now. Every time we open the door it tries to come in. We have two dogs and it's not afraid of them at all. We did try to put a bit food out for it , but we had to put it in a pet carrier at night because the local cats were trying to get it. We let it out first thing in the morning.  This was probably a mistake but we thought it was possibly injured. We now think it isn't and is flying about but comes straight back. Has anyone got any ideas or advice, it would be much appreciated.