Our conception of coreference is based on the notion of reference.
Reference is in general the relation of an expression to a real world object or situation. There are two main types of reference:
exophoric reference
= referring to a situation or entities outside the text (see Section 3.1.3, "Exophora").
endophoric reference
= referring to another expression within the same text
If two (or more) expressions occur in the text and refer to the same entity, situation etc. - i.e. they have the same reference - their relation (linking the utterances in the text) is called coreference.
As for the endophoric reference, an expression can refer to another expression in the preceeding (or subsequent) utterance or it can refer to a larger segment of the text, too.
NB! We are aware of the fact that the term coreference is usually used only for endophoric reference; still we use the term coreference for cases of extratextual reference as well.
Depending on the relative position of the expressions in the text, one can speak of anaphoric and cataphoric reference. If an expression refers to a preceding expression/utterance, it is a case of anaphoric reference. The expression that is referred to is called antecedent. Cataphoric reference refers to the following utterances or their parts; such an expression can be called postcedent.
Apart from these, other terms are also used: coreferring expression (element) - coreferred expression (element). These terms are more general and neglect the position of the expressions in the text - as both the antecedent and postcedent can be coreferred expressions.
Further, there is:
grammatical coreference (see Section 2, "Grammatical coreference").
textual coreference (see Section 3, "Textual coreference").
Both types are represented at the tectogrammatical level. The division of coreference into grammatical and textual is considered basic and all the other subdivisions take place within these two types.