Field theory MOC Category of fields The category of fields π₯π π½ is the subcategory of π±πππ containing only fields. ring Since field homomorphisms are injective, the only morphisms are field extensions, and are thus monic. By fixing a characteristic π, we may construct the subcategory Category of fields of characteristic p, and have π₯π π½=ββπ=0π₯π π½π tidy| en | SemBr