Prerequisites:

Description:

    Tensile strength is the ability for a material to be pulled in two different directions without breaking; ie to withstand tension.  This is a kind of broad category of materials which may have different origins.  The first relatively high-tensile strength material discovered was, arguably, steel.  Made into cables, steel is the main tensile component used today.  Another major one was carbon fiber, which of course came from organic chemistry and polymer research.  One powerful, but still (in the real world) impractical to manufacture option is Buckminster Fullerene tubes, or carbon nanotubes or pick your own preferred name for them.  Some sort of artificial evolution process could be made to work for folks who have biological computing or even just high levels of organic chemistry knowledge, as a means of finding higher tensile organic materials.
    The level of development available will depend on the levels given by the contributing theories.  This means that if one does not yet have the organic chemistry ability to figure out how to make carbon fiber, the High Tensile Strength Materials (dev) development category cannot progress to the range offered by that.  In other words, there will be a variety of specific levels granted by those theories which will allow the development of specific high tensile strength materials.
    There is no particular need for these materials to be discovered in the order from least-strength to most-strength.  It might very well be that a culture discovers carbon fiber before steel, for example.  In the long run, all of these areas should be split into their own technology pages, rather than the way I've specified, but I haven't yet figured out all of the possibliities.  Here is what I have (in order from least strenght to most):
Natural Organics (ie cotton/hemp rope, leather cored, whatever.  Pretty weak.)
Metal (Steel, aluminum, copper, alloys etc.  All give within an order of magnitude or two of the same strength)
Nylon, other artificial polymers
Carbon Fiber
(Pick your own artificial super-polymer)
Carbon Nanotube
Metallic Hydrogen
Nuclear Attraction Material (Tensile strength on the order of the interactions within an atomic nucleus. see Scrith in Niven books)
Stasis Chain (ie, a Niven-style stasis field around a chain, which'd give infinity tensile strength)