Electromagnetism can be generalized to Yang–Mills theory by replacing the group U(1) by a nonabelian Lie group. This raises the question of whether one can similarly generalize 2-form electromagnetism to a kind of ‘higher-dimensional Yang–Mills theory’. It turns out that to do this, one should replace the Lie group by a ‘Lie 2-group’, which is a category C where the set of objects and the set o...

The (dual) Dold-Kan correspondence says that there is an equivalence of categories K : Ch → Ab between nonnegatively graded cochain complexes and cosimplicial abelian groups, which is inverse to the normalization functor. We show that the restriction of K to DG-rings can be equipped with an associative product and that the resulting functor DGR → Rings, although not itself an equivalence, does ...

Abstract Let $$\mathbb {D}$$ D denote the unit disk of complex plane and let $$\mathcal {A}^2(\mathbb {D})$$ A 2 ( ) be Bergman space that consists those analytic functions on are integrable squar...

We provide conditions on a monoidal model categoryM so that the category of commutative monoids in M inherits a model structure from M in which a map is a weak equivalence or fibration if and only if it is so inM. We then investigate properties of cofibrations of commutative monoids, rectification between E∞-algebras and commutative monoids, the relationship between commutative monoids and mono...

Let $\mathcal{X}$ be a separable Hilbert space with norm $\|\cdot\|$ and let $T>0$. $Q$ linear, self-adjoint, positive, trace class operator on $\mathcal{X}$, $F:\mathcal{X}\rightarrow \mathcal{X}$ (smooth enough) function $W(t)$ $\mathcal{X}$-valued cylindrical Wiener process. For $\alpha\in [0,1/2]$ we consider the $A:=-(1/2)Q^{2\alpha-1}:Q^{1-2\alpha}(\mathcal{X})\subseteq \mathcal{X}\righta...