Add Functors to CatDat

[ScriptRaccoon]

Work in Progress

Related issue: #4

For functor implications, it is not sufficient to record the assumptions and the conclusion for the functor itself. We also need to record the assumptions of the source and the target category.

For example: the claim "a functor is continuous when it preserves products and equalizers" (which is often believed to be true) is actually false. We need to assume that the source category has products.

(
    'continuous_criterion',
    '["preserves products", "preserves equalizers"]', -- functor assumptions
    '["products"]', -- source assumptions
    '[]', -- target assumptions
    '["continuous"]', -- functor conclusions
    '... reason comes here ...', 
    FALSE
),

The Special Adjoint Functor Theorem is another good example.

    (
        'saft',
        '["continuous"]', -- functor assumption
        '["complete", "locally small", "well-powered", "cogenerator"]', -- source assumptions
        '["locally small"]', -- target assumption
        '["right adjoint"]', -- functor conclusion
        ' ... reference ...',
        FALSE
    );