Galois Categories
نویسنده
چکیده
In abstract algebra, we considered finite Galois extensions of fields with their Galois groups. Here, we noticed a correspondence between the intermediate fields and the subgroups of the Galois group; specifically, there is an inclusion reversing bijection that takes a subgroup to its fixed field. We notice a similar relationship in topology between the fundamental group and covering spaces. These ideas can be generalized and related using category theory, through the definition of a Galois category. Here we build up the basic theory necessary to understand and recognize these categories.
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