002_initial_objects.sql

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

INSERT INTO initial_objects (category_id, description)
VALUES
('1', 'the unique object'),
('Ab', 'trivial group'),
('Ab_fg', 'trivial group'),
('Alg(R)', '$R$'),
('Ban', 'trivial Banach space'),
('BanAlg_nu', 'zero algebra'),
('BanAlg_u', '$\mathbb{C}$'),
('CAlg(R)', '$R$'),
('Cat', 'empty category'),
('CMon', 'trivial monoid'),
('CRing', 'ring of integers'),
('CVNA', '$\mathbb{C}$'),
('FI', 'empty set'),
('FinAb', 'trivial group'),
('FinGrp', 'trivial group'),
('FinOrd', 'empty ordered set'),
('FinSet', 'empty set'),
('FreeAb', 'trivial group'),
('Grp', 'trivial group'),
('Haus', 'empty space'),
('LRS', 'empty space'),
('M-Set', 'empty set with the unique action'),
('Man', 'empty manifold'),
('Meas', 'empty set with the unique $\sigma$-algebra'),
('Met', 'empty metric space'),
('Met_c', 'empty metric space'),
('Met_oo', 'empty metric space'),
('Mon', 'trivial monoid'),
('N', '$0$'),
('N_oo', '$0$'),
('On', '$0$'),
('Pos', 'empty poset'),
('Prost', 'empty proset'),
('R-Mod', 'trivial module'),
('R-Mod_div', 'trivial module'),
('real_interval', '$0$'),
('Rel', 'empty set'),
('Ring', 'ring of integers'),
('Rng', 'trivial ring'),
('Sch', 'empty scheme'),
('Set', 'empty set'),
('Set*', 'singleton pointed set'),
('SetxSet', '$(0,0)$'),
('Sh(X)', 'constant sheaf with value $\varnothing$, sending all non-empty open sets to $\varnothing$ and the empty set to a singleton'),
('Sh(X,Ab)', 'trivial abelian sheaf'),
('Sp', 'species $X$ with $X_n = \varnothing$'),
('sSet', 'simplicial set $X$ with $X_n = \varnothing$'),
('Top', 'empty space'),
('Top*', 'singleton space with the unique base point'),
('Vect', 'trivial vector space'),
('walking_commutative_square', '$a$'),
('walking_isomorphism', 'both objects'),
('walking_fork', '$0$'),
('walking_morphism', '$0$'),
('walking_span', '$0$'),
('Z', 'constant functor with value $\varnothing$'),
('Z_div', '$1$'),
('walking_composable_pair', '$0$');

INSERT INTO special_objects
	(category_id, description, type)
SELECT
	category_id, description, 'initial object'
FROM initial_objects;

DROP TABLE initial_objects;