(My comment was generated by the spontaneous reaction and reflection of a native speaker rather than memory of any deliberately learned rule.) Wikipedia has this to say:
In English and some other languages, the use of such a word implies the definite article. For example, my car implies the car that belongs to me/is used by me; it is not correct to precede possessives with an article (* the my car) or other definite determiner such as a demonstrative (* this my car)
One should indeed think of " 's " in this context as the equivalent for nouns of what "my" is for the pronoun "I".
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Of course, for "every Monday", the last one should have been dated July 22-28. *cough*