Morphism of fusion systems
Suppose are both finite -groups (i.e., groups of prime power order for some prime number ). Suppose is a fusion system on and is a fusion system on . A morphism of fusion systems from to is a pair where:
- is a homomorphism of groups from to .
- is a covariant functor from the category to the category .
- For every subgroup , . Here, is the homomorphic image and is the image of the object under the covariant functor .
- If is a morphism in , then .