Congruent zeta functions. No.14

Yoshifumi Tsuchimoto

It is interesting to regard things in the language of category theory. We give here a brief, incomplete, incorrect list. The entry in $\mathbb{F}_1$ are here just for fun.

 
  $\mathbb{F}_1$ math $\mathbb{Z}$-modules affine schemes
modules   (Sets) (modules) (sheaves)
algebras   (monoid) ((unital) ring) (affine scheme)
      direct product disjoint union
      tensor product fiber product
morphisms   (map) (ring hom) (morphism)
      quotient map closed immersion
      localization by an element open immersion
      (Hopf algebra) (affine group scheme)
      (co-multiplication) (multiplication)
      (co-unit) (unit)
      (co-inverse) (inverse)