Functor

Functors encode invariants of isomorphism classes

Since functors take compositions to compositions and identities to identities, they also take isomorphisms to isomorphisms, thereby preserving isomorphism classes. #m/thm/cat

This is a fundamental idea that captures the very essence of what makes category theory useful. For example, in Topology MOC, the value an arbitrary functor assigns to any topological space is immediately a Topological property.¹

Fully faithful

If a functor is Fully faithful functor this becomes bidirectional:

#state/tidy | #lang/en | #SemBr