There is no right or wrong way to draft these agreements. But it makes a big difference if you retain ownership of the IP rights and license them to the company, and the company acquires ownership and licenses them to you. A non-exclusive licensee has no right to sue for infringement of intellectual property rights. Thus, if all you receive is a non-exclusive license to use the IP rights personally or in your business, you lose the right to sue others for infringement. You also lose the right to license your IP rights to others (including competitors of the company). The company is not necessarily trying to "screw you", but it want to control the IP rights, decide who to sue for infringement, and decide whether and who to grant other licenses of the IP rights. If your ownership rights are stripped away in this manner, all you are left with is a non-exclusive right to use the IP rights. This probably is not what you had in mind.
Trust me about this----these agreements are complex and it takes years of experience to understand them even for trained lawyers. You need to retain a lawyer to negotiate this agreement for you----you obviously cannot do this yourself.
This sounds like you were hired by these colleagues to create this work as an employee of their company, and under general agency law, your employer would own the proceeds in the work you did.
But you seem to think you should still retain ownership rights, while giving the company a non-exclusive license to use your work.
Apparently this wasn't discussed and agreed on BEFORE you were hired. This is something that needs to be negotiated. Your bargaining position is better if you weren't paid, or weren't paid much, which might imply that the parties expected you to retain some rights. But if you were paid for your work, the opposite is true. At any rate, if their proposal gives you a, irrevocable license for your work, and the ability ot sub-license it to others, it amounts to the same thing, since both parties contemplated that the other would be able to use your work in perpetuity.
See a business/IP lawyer for help to make sure that what you're signing reflects what you intend.
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I see no reason for you to sign anything.
If you were truly an employee when you co-authored the computer program then Attorney Koslyn is certainly correct -- you are not an owner of the copyright in the computer program [your employer is the sole owner] and so have nothing to assign to the new company.
But there are at least two other alternatives:
1. You and the others who co-authored the program created a partnership or joint venture when you worked together to co-author the program. The creation of either cannot be done, for copyright purposes, orally but rather could be done if a writing of some kind establishes either [the writing could be more than one, taken together, but must memorialize an agreement that you were all working together in order to create something for which you all, as a group, would commercialize somehow]. If that is the case then NONE of you own a copyright interest in the program: The owner is the partnership or joint venture. So, again, you have nothing to assign to the new company. What you have is an undivided interest in the assets of the partnership or joint venture -- the assets being at least the copyright in the program and quite probably other things of value.
2. You co-authored the program in your own individual capacity. If that's the case, then as a joint author you own an undivided interest in the copyright that attaches to the program [the entire program, not just your contribution, if all of you intended that each of your contributions would function together]. You DO NOT need a license to make use of your own copyright because each joint author can do with the work whatever he or she wants to [except sell the copyright or exclusively license it to someone else]. So the assignment - license back agreement makes absolutely NO SENSE for you. You don't need a license. And why you would want to assign [i.e., sell] your ownership in the copyright to the program is beyond me unless you're paid handsomely.
Speak with a copyright attorney licensed to practice in your state. The first step is to determine if you were an employee, member of a partnership or joint venture, or an individual joint author. Only then can you figure out whether you own a copyright interest in the program -- or maybe just the part you created.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.