That depends on your definition of Anarcho-syndicalism.
For some Anarcho-syndicalists, seizing the factories is it. The workers then 'own' those workplaces and can trade with other self-managed workplaces. Like a series of co-operatives covering the world. 'The mines for the miners' and all that. In the end, these self-managed workplaces can reproduce capitalist relations,
go war with each other or whatever, it's not up to anyone else to tell the workers in that workplace not to be massive shitbags.
For some Anarchist-Communists, Anarcho-syndicalism is a tactic - it will be through revolutionary union organisation at the workplace that capitalism will be overthrown.
Then there are Anarcho-syndicalists that more-or-less ascribe to the Anarchist-Communist view; and there are Anarchist-Communists that reject Anarcho-syndicalism at all.
In Russia in 1917 there was a split between the Anarcho-syndicalists who wanted to organise through unions and those who wanted to organise through soviets.
It's all a bit of a mix really.


