In category theory, each functor defines an invariant, but not all invariants are functional
Can you give some examples when
- a functor is an invariant
- an invariant is a functorial
- an invariant is not functorial
I also need another example:
– a functor is not an invariant $ => $ it's absurd and false but I need you to show me the underlying contradiction
For $ A $ a monoid equipped with an action on an object $ V $, a invariant of action is a generalized element of $ V $ which is taken by the action to itself, hence a fixed point for all operations in the monoid.
A action of a category $ C $ on a tray $ S $ nothing is more than one functor $ rho: C to $ Together.