Smooth Manifolds
... Lorentz metric, whose curvature results in gravitational phenomena. In such a model there is no physical meaning that can be assigned to any higher-dimensional ambient space in which the manifold lives, and including such a space in the model would complicate it needlessly. For such reasons, we need ...
... Lorentz metric, whose curvature results in gravitational phenomena. In such a model there is no physical meaning that can be assigned to any higher-dimensional ambient space in which the manifold lives, and including such a space in the model would complicate it needlessly. For such reasons, we need ...
First-Order Logical Duality Henrik Forssell
... an equivalence between the ‘syntactical’ and ‘semantical’ subcategories of theories and models. Full first-order theories, too, form a category when considered up to algebraic equivalence, namely the category of Boolean coherent categories and coherent functors between them. This category contains t ...
... an equivalence between the ‘syntactical’ and ‘semantical’ subcategories of theories and models. Full first-order theories, too, form a category when considered up to algebraic equivalence, namely the category of Boolean coherent categories and coherent functors between them. This category contains t ...
Fascicule
... B2 such that gη = g. It is easily proven that ηe is an epic in B and, since m = g(ηe) we see that ηe is a right factor of m in the subcategory B . This implies that ηe is invertible, and that (ηe)−1 η is a left inverse for e. But then e is an epic with a left inverse which implies that e is invertib ...
... B2 such that gη = g. It is easily proven that ηe is an epic in B and, since m = g(ηe) we see that ηe is a right factor of m in the subcategory B . This implies that ηe is invertible, and that (ηe)−1 η is a left inverse for e. But then e is an epic with a left inverse which implies that e is invertib ...
