Related papers: A BV-Category of Spacetime Interventions
Automation of tasks can have critical consequences when humans lose agency over decision processes. Deep learning models are particularly susceptible since current black-box approaches lack explainable reasoning. We argue that both the…
We describe an algebraic chain level construction that models the passage from an arbitrary topological space to its free loop space. The input of the construction is a categorical coalgebra, i.e. a curved coalgebra satisfying certain…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
Cubical type theory provides a constructive justification to certain aspects of homotopy type theory such as Voevodsky's univalence axiom. This makes many extensionality principles, like function and propositional extensionality, directly…
We introduce a constructive procedure that maps all spatial correlations of a broad class of states into temporal correlations between general quantum measurements. This allows us to present temporal phenomena analogous to genuinely…
We show that one can use model categories to construct rational orthogonal calculus. That is, given a continuous functor from vector spaces to based spaces one can construct a tower of approximations to this functor depending only on the…
Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body…
We propose a layered hierarchical architecture called UCLA (Universal Causality Layered Architecture), which combines multiple levels of categorical abstraction for causal inference. At the top-most level, causal interventions are modeled…
We prove an integral representation result for variational functionals in the space $BV^{\mathcal{B}}$ of functions with bounded $\mathcal{B}$-variation where $\mathcal{B}$ denotes a $k$-th order, $\mathbb{C}$-elliptic, linear homogeneous…
One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and outputs. Given a functor $L \colon…
We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a combinatorial construction (blocker duality) which yields…
This paper is a continuation of a previous paper of the author, which gave an analogue to the classical Schur-Weyl duality in the setting of Deligne categories. Given a finite-dimensional unital vector space $V$ (a vector space $V$ with a…
We generalize the BV formalism for the physical theories on supermanifolds with graded symmetry algebras realized off-shell and on-shell. An application of such generalization to supersymmetric theories allows us to formulate the new…
We give a general method to build categories of combinatorial manifolds, i.e. categories of combinatorial objects satisfying some local property at every "point", as coreflective subcategories of categories of relational presheaves. To do…
We construct super-version of Quantum Representation Theory. The quadratic super-algebras and operations on them are described. We also describe some important monoidal functors. We proved that the monoidal category of graded super-algebras…
Modern programming frequently requires generalised notions of program equivalence based on a metric or a similar structure. Previous work addressed this challenge by introducing the notion of a V-equation, i.e. an equation labelled by an…
In the present study, we use cross-domain classification using quantum machine learning for quantum advantages to readdress the entanglement versus separability paradigm. The inherent structure of quantum states and its relation to a…
Using the symmetric monoidal closed category structure of the category of measurable spaces, in conjunction with the Giry monad which we show is a strong monad, we analyze Bayesian inference maps and their construction in relation to the…
In the well-known settings of category theory enriched in a monoidal category V, the use of V-enriched functor categories and bifunctors demands that V be equipped with a symmetry, braiding, or duoidal structure. In this paper, we establish…
Double-bosonisation associates to a braided group in the category of modules of a quantum group, a new quantum group. We announce the semiclassical version of this inductive construction.