Yes, you can run Ethernet from your home router to your shed.
Ideally you’d use conduit to protect the cable, or use Ethernet cable designed for outdoor use. However, I’ve seen normal Ethernet cables last 10+ years outside without issue.
As others have mentioned, ideally the router in the shed will have DHCP turned off, and the incoming line will go into one of the normal Ethernet ports (not the WAN/Internet port). This will allow two-way communication between your house and shed (IE, your computers, network drives, network printers, network cameras, etc. can all see each other no matter which router they are connected to). However, if you only need Internet you can just plug the Ethernet cable into the WAN/Internet port on the shed’s router.
Yes, you can run Ethernet from your home router to your shed.
Ideally you’d use conduit to protect the cable, or use Ethernet cable designed for outdoor use. However, I’ve seen normal Ethernet cables last 10+ years outside without issue.
As others have mentioned, ideally the router in the shed will have DHCP turned off, and the incoming line will go into one of the normal Ethernet ports (not the WAN/Internet port). This will allow two-way communication between your house and shed (IE, your computers, network drives, network printers, network cameras, etc. can all see each other no matter which router they are connected to). However, if you only need Internet you can just plug the Ethernet cable into the WAN/Internet port on the shed’s router.