Is the noun process an abstract noun?

Yes, the noun 'process' is an abstract noun as a Word for a continuing action or series of actions or changes; a Word for the carrying out of a legal action; a Word for a concept.

The noun 'process' is a concrete noun as a Word for an appendage or outgrowth or protuberance on or in an organism; a Word for a physical thing.

The Word 'process' is also a verb: process, processes, processing, processed.