003_terminal_objects.sql

CREATE TEMP TABLE terminal_objects (
    category_id TEXT NOT NULL,
    description TEXT NOT NULL
);

INSERT INTO terminal_objects (category_id, description)
VALUES
('1', 'the unique object'),
('Ab', 'trivial group'),
('Ab_fg', 'trivial group'),
('Alg(R)', 'trivial algebra'),
('Ban', 'trivial Banach space'),
('BanAlg_nu', 'zero algebra'),
('BanAlg_u', 'zero algebra'),
('CAlg(R)', 'trivial algebra'),
('Cat', '<a href="/category/1">trivial category</a>'),
('CMon', 'trivial monoid'),
('CRing', 'zero ring'),
('CVNA', 'zero algebra'),
('FinAb', 'trivial group'),
('FinGrp', 'trivial group'),
('FinOrd', 'singleton ordered set'),
('FinSet', 'singleton set'),
('FreeAb', 'trivial group'),
('Grp', 'trivial group'),
('Haus', 'singleton space'),
('LRS', '$\mathrm{Spec}(\mathbb{Z})$'),
('M-Set', 'singleton set with the unique action'),
('Man', 'singleton manifold of dimension $0$'),
('Meas', 'singleton set with the unique $\sigma$-algebra'),
('Met', 'singleton space'),
('Met_c', 'singleton space'),
('Met_oo', 'singleton space'),
('Mon', 'trivial monoid'),
('N_oo', '$\infty$'),
('Pos', 'singleton poset'),
('Prost', 'singleton proset'),
('R-Mod', 'zero module'),
('R-Mod_div', 'zero module'),
('real_interval', '$1$'),
('Rel', 'empty set'),
('Ring', 'zero ring'),
('Rng', 'zero ring'),
('Sch', '$\mathrm{Spec}(\mathbb{Z})$'),
('Set', 'singleton set'),
('Set*', 'singleton pointed set'),
('Setne', 'singleton set'),
('SetxSet', '$(1,1)$'),
('Sh(X)', 'constant sheaf with value a singleton'),
('Sh(X,Ab)', 'trivial abelian sheaf'),
('Sp', 'species $X$ with $X_n = 1$'),
('sSet', 'simplicial set $X$ with $X_n = 1$'),
('Top', 'singleton space'),
('Top*', 'singleton space with the unique base point'),
('Vect', 'trivial vector space'),
('walking_commutative_square', '$d$'),
('walking_isomorphism', 'both objects'),
('walking_morphism', '$1$'),
('Z', 'constant functor with value $1$'),
('Z_div', '$0$'),
('walking_composable_pair', '$2$');

INSERT INTO special_objects
	(category_id, description, type)
SELECT
	category_id, description, 'terminal object'
FROM terminal_objects;

DROP TABLE terminal_objects;