The Mishnah (6:1) teaches that the mitzvah of yibum is performed whether it was done so, deliberately (mezid) inadvertent (shogeg), whether it was forced or performed willingly.
Rashi (53b) explains that the case of shogeg, is where the brother that performed yibum, thought that the yabam was his wife or someone else. The difficulty is that Rashi explains that the case of mezid is where he had the relationship, but not for the purpose of the mitzvah but rather zenut. It would seem that Rashi's explanation of shogeg as where he thought it was someone else would also be considered a case of zenut. The Tosfot Yom Tov therefore explains that the difference between shogeg and mezid is that in the case of shogeg the identities are mistaken, whereas for mezid, the identities are known, however the intentions at the time of yibum was not for the mitzvah.
The Minchat Chinnuch (598:6) however finds this Mishnah difficult. He notes that most rishonim rule that mitzvot tzrichot kavana -- one has to have intention to fulfill a mitzvah when performing it in order for the mitzvah to be fulfilled. He continues that even according to the opinions that kavana is not required, "anti-kavana", having the express intent not to perform the mitzvah would prevent its fulfillment. That being the case, it is difficult to understand how the mitzvah of yibum is fulfilled in the cases of shogeg and mezid.
The Minchat Chinnuch continues by noting that the Gemara derives the law in our Mishnah from pesukim in the Torah. Consequently, he explains that even though yibum would work in these cases and they would now be considered married, the mitzvah would have not been fulfilled. They would have to have another relationship with the intent to fulfill the mitzvah for the mitzvah to be fulfilled. He explains that a practical implication of this understanding is they would not be able to get divorced immediately after a yibum that was shogeg or meizid, with performing the mitzvah.
Interestingly, in the footnotes in the Machon Yerushalaim edition (8) there is a note that if they are already considered married, then the zika (the bond that obligates yibum or chalitzah) is no longer present. That being the case, how then could the mitzvah of yibum be fulfilled even if it is followed with the intention to fulfill the mitzvah?
The Kovetz Shiurim (Ketuvot 249) however explains that since the kinyan (that which makes them considered married) does not require kavana, the mitzvah is also fulfilled. Based on this, the Kovetz Shiurim differentiates more broadly in the law regarding mitzvot tzrichot kavana. He explains, that according to the opinion that requires kavana, there is a difference whether the act itself is the mitzvah or whether the outcome is a mitzvah. If the act is a mitzvah, for example eating matzah or blowing shofar, then intent is necessary. If however the main part of the mitzvah is the outcome, then intent at the time of the act is not critical. He uses the example of the mitzvah of having children. Even if there was no intent at the time of conception to fulfill the mitzvah, the mitzvah is nonetheless fulfilled.1
1 The Kovetz Shiurim continues that it is possible that this distinction also applies regarding the issue of mitzvah haba'ah be'aveirah. For example, he suggests that even if one's child was a mamzer, they would still have fulfilled the mitzvah of peru urvu.
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