Category of fields of characteristic $𝑝$

The category of fields of characteristic $𝑝$ $𝖥 𝗅 𝖽 𝑝$ is the subcategory of $𝖥 𝗅 𝖽$ consisting of just those of characteristic $𝑝$ . #m/def/field These subcategories are completely disjoint in $𝖥 𝗅 𝖽$ , thus

𝖥 𝗅 𝖽 = \infty ∐ 𝑝 = 0 𝖥 𝗅 𝖽 𝑝

where $𝖥 𝗅 𝖽 𝑝$ is empty iff $𝑝$ is not prime.

Properties

The initial object of $𝖥 𝗅 𝖽 𝑝$ is $ℚ$ if $𝑘 = 0$ or $ℤ 𝑝$ if $𝑝$ is prime by A field contains $ℤ 𝑝$ or $ℚ$ .

#state/develop | #lang/en | #SemBr

Category of fields of characteristic 𝑝

Properties

Category of fields of characteristic $𝑝$