It is my understanding that restrictions and prohibitions on the Sabbath more accurately concern "creating" or "destroying" rather than the stereotypical concept of "working". Why is it then acceptable to have relations since such is an act of "creating"? In fact, if I understand correctly, husband and wife relations on the Sabbath is considered a mitzvah. Thank you for your response (s).
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On Shabbat, one is not prohibited from doing all creative work, only that which fall into one of the 39 Categories. These categories were determined based on the creative work necessary for the construction of the Mishkan (Tabernacle), and since procreation was not necessary for the construction, it is not prohibited.
In addition, it is unclear if sexual relations are an act of creation. It is not guaranteed the relations on Shabbat will lead to a conception, and even if it did, the rabbis held that an embryo isn't viable until 40 days after conception.
Regarding the Mitzvah aspect:
This was codified by the Shulchan Aruch (Orach Chaim 280:1)
Additional information can be found at: http://www.thejc.com/judaism/rabbi-i-have-a-problem/68658/why-sex-allowed-shabbat
There is an interesting article at http://thetorah.com/intimacy-on-shabbat which explains that some Second Temple sects believed sex to be prohibited on Shabbat.
As Shmuel wrote, relations does not involve any of the 39 forbidden activities and is not forbidden.
I would like to add a few additional thoughts: