Related papers: Base change along lax squares
The $\lambda$$\Pi$-calculus modulo theory is an extension of simply typed $\lambda$-calculus with dependent types and user-defined rewrite rules. We show that it is possible to replace the rewrite rules of a theory of the…
We give a new Littlewood-Richardson rule for the Schubert structure coefficients of isotropic Grassmannians, equivalently for the multiplication of $P$-Schur functions. Serrano (2010) previously gave a formula in terms of classes in his…
Building on Power's notion of a pasting diagram, we prove a pasting theorem for categories enriched in quasi-categories.
We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any…
Using the complex stereographic variable representation for the macrospin, from a study of the nonlinear dynamics underlying the generalized Landau-Lifshitz(LL) equation with Gilbert damping, we show that the spin-transfer torque is…
Via the adjunction $ - \boldsymbol{\cdot} 1 \dashv \mathcal V(1,-) \colon \mathsf{Span}(\mathcal V) \to \mathcal V \text{-} \mathsf{Mat} $ and a cartesian monad $ T $ on an extensive category $ \mathcal V $ with finite limits, we construct…
In this paper, we investigate the relationship between two elementary operations on derivations in the framework of graph transformation based on adhesive categories: moving a derivation along a derivation based on parallel and sequential…
The shift locus is the space of normalized polynomials in one complex variable for which every critical point is in the attracting basin of infinity. The method of sausages gives a (canonical) decomposition of the shift locus in each degree…
We discuss the general theory of realizing two-variable fuctions on slide rules (based on our paper 1977) and offer some new scales for practical use.
We investigate generally covariant theories which admit a Fierz-Pauli mass term for metric perturbations around an arbitrary curved background. For this we restore the general covariance of the Fierz-Pauli mass term by introducing four…
Using nonstandard recursion relations for Fresnel coefficients involving successive stacks of layers, we extend the Lifshitz formula to configurations with an inhomogeneous, n-layered, medium separating two planar objects. The force on each…
A comprehensive account of the categorical properties of the category of small categories and asymmetric delta lenses is given in the recent works of Chollet et al. and Di Meglio. An important construction for proving many of these…
We study properties of a category after quotienting out a suitable chosen group of isomorphisms on each object. Coproducts in the original category are described in its quotient by our new weaker notion of a 'phased coproduct'. We examine…
A planar tree power series over a field $K$ is a formal expression $$\sum c_T \cdot T$$ where the sum is extended over all isomorphism classes of finite planar reduced rooted trees $T$ and where the coefficients $c_T$ are in $K$.…
An algorithm is described for the construction of actions for scalar, spinor, and vector gauge fields that remains well-defined when the metric is degenerate and that involve no contravariant tensor fields. These actions produce the…
We prove a generalization of a theorem of Bunge and Gray about forming colax adjunctions out of relative Kan extensions and apply it to the study of the Kleisli 2-category for a lax-idempotent pseudomonad. For instance, we establish the…
We prove that strictly convex surfaces moving by $K^{\alpha/2}$ become spherical as they contract to points, provided $\alpha$ lies in the range $[1,2]$. In the process we provide a natural candidate for a curvature pinching quantity for…
String-inspired cosmologies, whereby a non-singular curvature bounce is induced by a general-covariant, $T$-duality-invariant, non-local dilaton potential, are used to study numerically how inhomogeneities evolve and to compare the outcome…
In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain an ambient category in which we determine subcategories…
The Gromov-Witten invariants of a smooth, projective variety $V$, when twisted by the tautological classes on the moduli space of stable maps, give rise to a family of cohomological field theories and endow the base of the family with…