Author: jonatan Format: TextIs it possible to infer morphisms and properties of the higher order categories from the properties and morphisms of the lower order categories? Are there applications of such kind of zooming or microscopy in math? I have recently read about logic as category which has statements as objects and derivation relation as morphisms. But recently I also found different look on logics - there are categories whose objects are whole logics and morphisms are translations among logics. Apparently one can construct here lkower-higher order category structures and make lot of theory and applications. Is that possible and is it wise endeavour to pursue?
References:
John L. Bell.The Development of Categorical Logic - logic as category
Peter Arndt. Homotopical Categories of Logics - category of logics
Is it possible to infer morphisms and properties of the higher order categories from the properties and morphisms of the lower order categories? Are there applications of such kind of zooming or microscopy in math? I have recently read about logic as category which has statements as objects and derivation relation as morphisms. But recently I also found different look on logics - there are categories whose objects are whole logics and morphisms are translations among logics. Apparently one can construct here lkower-higher order category structures and make lot of theory and applications. Is that possible and is it wise endeavour to pursue?
References: John L. Bell.The Development of Categorical Logic - logic as category Peter Arndt. Homotopical Categories of Logics - category of logics