Related papers: Sigma limits in 2-categories and flat pseudofuncto…
Filinski constructed a symmetric lambda-calculus consisting of expressions and continuations which are symmetric, and functions which have duality. In his calculus, functions can be encoded to expressions and continuations using primitive…
The familiar construction of categories of fractions, due to Gabriel and Zisman, allows one to invert a class W of arrows in a category in a universal way. Similarly, bicategories of fractions allow one to invert a collection of arrows in a…
The physical meaning of the Levi-Civita spacetime for some "critical" values of the parameter sigma, is discussed in the light of gedanken experiments performed with gyroscopes circumventing the axis of symmetry. The fact that sigma=1/2…
In [Homotopical Algebra, Springer LNM 43] Quillen introduces the notion of a model category: a category $\mathcal{C}$ provided with three distinguished classes of maps $\{\mathcal{W},\, \mathcal{F},\, co\mathcal{F}\}$ (weak equivalences,…
We introduce pseudoalgebras for relative pseudomonads and develop their theory. For each relative pseudomonad $T$, we construct a free--forgetful relative pseudoadjunction that exhibits the bicategory of $T$-pseudoalgebras as terminal among…
A pseudomonad on a $2$-category whose underlying endomorphism is a $2$-functor can be seen as a diagram $\mathbf{Psmnd} \rightarrow \mathbf{Gray}$ for which weighted limits and colimits can be considered. The $2$-category of pseudoalgebras,…
We study N=(0,2) deformed (2,2) two-dimensional sigma models. Such heterotic models were discovered previously on the world sheet of non-Abelian strings supported by certain four-dimensional N=1 theories. We study geometric aspects and…
We study a one parameter family of supersymmetric marginal deformations of ${\cal N}=4$ SYM with $U(1)^3$ symmetry, known as $\beta$-deformations, to understand their dual $AdS\times X$ geometry, where $X$ is a large classical geometry in…
We study ruled submanifolds of Euclidean space. First, to each (parametrized) ruled submanifold $\sigma$, we associate an integer-valued function, called degree, measuring the extent to which $\sigma$ fails to be cylindrical. In particular,…
In this paper we investigate the behavior of the sigma function over the family of cyclic trigonal curves $X_s$ defined by the equation $y^3 =x(x-s)(x-b_1)(x-b_2)$ in the affine $(x,y)$ plane, for $s\in D_\varepsilon:=\{s \in \mathbb{C} |…
In this paper we present some linear algebra behind quadratic parts of quadratically flat complex points of codimension two real submanifold in a complex manifold. Assuming some extra nondegenericity and using the result of Hong, complete…
We introduce a candidate for the inner hom for $Dbl^{st}_{lx}$, the category of strict double categories and lax double functors, and characterize a lax double functor into it obtaining a lax double quasi-functor. The latter consists of a…
By the biadjoint triangle theorem, given a pseudomonad $\mathcal{T} $ on a $2$-category $\mathfrak{B} $, if a right biadjoint $\mathfrak{A}\to\mathfrak{B} $ has a lifting to the pseudoalgebras…
The tensor functor called $\alpha$-induction produces a new unitary fusion category from a Frobenius algebra, or a $Q$-system, in a braided unitary fusion category. A bi-unitary connection, which is a finite family of complex number subject…
We study the convolution of functions of the form \[ f_\alpha (z) := \dfrac{\left( \frac{1 + z}{1 - z} \right)^\alpha - 1}{2 \alpha}, \] which map the open unit disk of the complex plane onto polygons of 2 edges when $\alpha\in(0,1)$. We…
Double sigma model with the strong constraints is equivalent to the normal sigma model by imposing the self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We…
We prove that the doubly lambda-deformed sigma-models, which include integrable cases, are canonically equivalent to the sum of two single lambda-deformed models. This explains the equality of the exact beta-functions and current anomalous…
The main purpose of this article is to extend some of the ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. Given a generic component of the…
We introduce some deformations of the biset category and prove a semisimplicity property. We also consider another group category, called the subgroup category, whose morphisms are subgroups of direct products, the composition being star…
A lattice formulation of the $O(1,2)/O(2)\times Z_2$ sigma model is developed, based on the continuum theory presented in the preceding paper. Special attention is given to choosing a lattice action (the ``geodesic'' action) that is…