4 ms·
What exactly would be the benefit of using category theory? What would you gain in comparison to doing just normal homomorphisms? And that's even assuming you w
by jkbyc 14y ago
What exactly would be the benefit of using category theory? What would you gain in comparison to doing just normal homomorphisms? And that's even assuming you would be able to find a homomorphism at all; it may well be prevented by the ontologies being mutually inconsistent, right?
- Dn_Ab 14y agoThe benefit is its flaw. Because it is so abstract it is able to describe many, many things. It can serve as a basis for all of maths and unlike set theory really focuses on structure. Very roughly, think of it like functional programming to Set theory's imperative nature.
- blair_strang 14y agoI'm not getting your analogy :/
- Dn_Ab 14y agoIt is not a tight analogy. But: In set theory you pay a lot of attention to the internals of collections of objects. In category theory you are more interested in capturing structure and relationships. In imperative programming you specify the internal sequence that makes up an operation, in functional programming you are more interested in the high level declarations, compositions and that the constraints on them are satisfied.
- jasomill 14y agoYou gain proofs that apply to a wider variety of algebraic structures.