Congruent zeta functions. No.09

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)