By "foundation of narratology," I am supposing you mean the essential components of narratological study rather than the historical background that begins with Russian Formalists and sembiotcs (i.e., the study of signs, as in signifiers). Proceeding on this supposition, narratology primarily has its foundation in the (1) universality of narrative, whether oral, film, song, or written, etc; the (2) temporal structure of narrative, which applies to chronology, analepsis and prolepsis (i.e., flashback and flashforward); the (3) narrative structure; the (4) narrative function (i.e., pertaining to actants, not "purpose"); and the (5) cultural relationship of narrative.
Narrative, a universal experience across cultures and across genres, from fairy tale to sitcom, is traditionally founded in identifying the the formal and structural parts of a narrative, relevant to the narrative "grammar," though there are expanding schools that seek to include "dynamic" discourse in narratological study. This traditional emphasis reflects narratology's origins in Formalism that analyzes literature from within its devices, irony, etc.
In narratology, questions of chronological structure are very important because this is relevant to the focalization of a narrative: Who is focalizing attention as the focalizer on what focalized object (including actant) or event, and to what past, present, or future time is the focalization oriented? Within this framework, the narrative function of the actants is crystallized: Is the actant a hero, a villain, a message bringer, or serving some other function within the narrative? The spatial orientation of the narrator/focalizer (i.e., diegesis) provides information on objectivity, point of view, and reliability: e.g., is the diegesis oriented as metadiegetic with narrator focalization from within the narrative (e.g., Heart of Darkness), or is it extradiegetic with narrator focalization from without the narrative (e.g., Sense and Sensibility)?
The reader is the decoder of the narratological code/signs and is relevant to the relationship between narrative and culture. The decoder/reader might feel uneasiness due to a narrative. Uneasiness might come from (1) unanswered questions that are raised in the decoder's mind or from (2) unresolved anticipation of upcoming events (i.e., hermeneutic or proairetic code). While the role of the decoder is subject to much debate and (sometimes) authorial distress because of the theoretically unlimited possibilities of author/decoder "coproduction" (i.e., interpretation and assignment of meaning), a production like James's The Turn of the Screw seems to have a universal effect of uneasiness on readers within Western culture.
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