Factory injection type is mostly used when we need to place into container objects of classes we did not created. Fore example objects from cocoa, or another 3rd party code.
Simply must be created factory class, which create object you need. Factory class must implement -(id)createInstance method, where object is created.

Define factory which is added to container

@implementation LabelsFactory
- (id)createInstance {
    UILabel *label = [[[UILabel alloc] init] autorelease];
    label.text = @"From factory";
    [label sizeToFit];
    return label;
}
@end

Add component with factory injection type

[[self.container withInjectionType:MVIOCFactoryInjectionTypeDefault] addComponent:[LabelsFactory class] representing:[UILabel class]];

MVIOCFactoryInjectionTypeDefault is macro, creating factory injection type with 'factory object injection type' setted to property injection type. What does it means? It means, that factory object which is created and upon which is called createInstance, can be filled with dependecies from container, as any other component inside container.