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Are all AGM batteries deep cycle?

I think that there are AGM batteries that are dual-purpose and can be used for both i.e. starting as well as deep cycle applications. But I want to ask you people about such AGM batteries that are intended for using only as a starting battery and cannot withstand being fully discharged. Are there such AGM batteries? Could you enlighten me on these batteries? I would like to hear soon from you guys. Thanks.