diff --git a/databases/catdat/data/category-implications/algebraic.yaml b/databases/catdat/data/category-implications/algebraic.yaml index 759ea038..8b02da58 100644 --- a/databases/catdat/data/category-implications/algebraic.yaml +++ b/databases/catdat/data/category-implications/algebraic.yaml @@ -24,15 +24,6 @@ reason: The regular epimorphisms are precisely the sort-wise surjective homomorphisms, which are clearly stable under pullbacks. is_equivalence: false -- id: algebras_with_0_disjoint_products - assumptions: - - finitary algebraic - - pointed - conclusions: - - disjoint products - reason: 'We have a constant in every algebra, let us denoted it by $0$. Then the projection $A \times B \to A$ is clearly surjective, hence an epimorphism. To show that $A \sqcup_{A \times B} B$ is trivial, let $R$ be an algebra which admits homomorphisms $f : A \to R$, $g : B \to R$ such that $f(p_1(a,b)) = g(p_2(a,b))$ for all $(a,b) \times A \times B$. This means $f(a) = g(b)$. In particular, $f(a) = g(0) = 0$. Likewise, $g(b) = 0$, and we are done.' - is_equivalence: false - - id: generalized_variety_require_sifted_colimit assumptions: - generalized variety diff --git a/databases/catdat/data/category-implications/thin.yaml b/databases/catdat/data/category-implications/thin.yaml index 46d0f256..47b161b9 100644 --- a/databases/catdat/data/category-implications/thin.yaml +++ b/databases/catdat/data/category-implications/thin.yaml @@ -7,16 +7,9 @@ - generating set - locally essentially small - one-way - reason: This is trivial. The empty set is generating. - is_equivalence: false - -- id: thin_consequence - assumptions: - - thin - conclusions: - equalizers - left cancellative - reason: Any two parallel morphisms are equal, so their equalizer is the identity, and every morphism is a monomorphism as well. + reason: This is trivial. is_equivalence: false - id: thin_inhabited_consequence diff --git a/src/components/Selection.svelte b/src/components/Selection.svelte index 01834f2a..114c816c 100644 --- a/src/components/Selection.svelte +++ b/src/components/Selection.svelte @@ -1,7 +1,7 @@