Quantum information effects

We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including measurement. We provide universal categorical constructions that semantically interpret this arrow metalanguage with choice, starting with any rig groupoid interpreting the reversible base language. Several properties of quantum measurement follow in general, and we translate (noniterative) quantum flow charts into our language. The semantic constructions turn the category of unitaries between Hilbert spaces into the category of completely positive trace-preserving maps, and they turn the category of bijections between finite sets into the category of functions with chosen garbage. Thus they capture the fundamental theorems of classical and quantum reversible computing of Toffoli and Stinespring.

“Masking” Makeup: Cosmetics and Constructions of Race in Rio de Janeiro

This article examines applications of bright, eye-catching makeup on the periphery of Rio de Janeiro, Brazil. Tracking the aesthetic decisions of makeup artists and their clients, I analyze how colorful manipulations of the bodily surface relate to local constructions of race. But the bodily surface does not simply reflect established and conventional understandings of race, nor are the aesthetics described herein merely symbolic of assumptions of difference. Instead, the aesthetic practices portrayed in this article may also be regarded as experimental, “nondiscursive” moments—operating on a complementary semiotic register—in the production of yet-to-be actualized ideas about race and being. This research shows how makeup practices often disrupt the aesthetic and conceptual links that tie insides to outsides, essences and souls to physical appearance, and in so doing chip away at the foundations on which race in Brazil has historically been built. Through sixteen months of ethnographic fieldwork (2019–2020) in Rio’s northern suburbs, I observed as disparate aesthetic practices—namely, beautification and transformation—merged with eclectic understandings of the body and notions of being. Through these alternating lenses, makeup enthusiasts often interpreted material signs of the body as pointing to categorical constructions of race, on the one hand, and to beauty, sex, and desire, on the other.These semiotic oscillations and their interpretations often stood in conflict with established racial discourses, and yet rather than being exceptional, I argue that such exploratory, sensuous aesthetics are in fact mundane. Taking as a starting point the understanding that racial discourse in Brazil, as elsewhere, is internally ambiguous and rife with epistemic conflict, this article describes nondiscursive aesthetic practices as strands of material disorder—latent with possibility but often incongruous with what we think we know about race—working to forge novel understandings of race, beauty, and the body.

Categorical definitions and properties via generators

In the present work, we show how the study of categorical constructions does not have to be done with all the objects of the category, but we can restrict ourselves to work with families of generators. Thus, universal properties can be characterized through iterated families of generators, which leads us in particular to an alternative version of the adjoint functor theorem. Similarly, the properties of relations or subobjects algebra can be investigated by this method. We end with a result that relates various forms of compactness through representable functors of generators.

Characteristics of the paradigm of the category of voice in the Old Saxon language

The article attempts to characterize the paradigm of the category of the voice of the Old Saxon language, based on the texts of the ancient saxon poem “The Savior” (“Heliand”). The author states that the category of the voice of the Old Saxon language was represented by pre-categorical inverse constructions with reflexive, reciprocal and inverse shades and participle passive constructions, namely copulative structures “to be / become” + II participle and non-copulative participle structures that broadcast different types of voice relations. It is proved that the active voice of the Old Saxon language was represented by the indicative (real voice), with the subject that was an active performer of the action. In particular, the active voice structures could be factual (agential). As in other Old Germanic languages, in the Old Saxon language the active voice expresses the reality of action, events, their prediction and shades of command. In particular, it is determined in the article that as an opposition of active voice were grammatical constructions that had shades of reversion (inverse, reciprocal, inverse), the so-called “branching” in shades of voice values: the actual inverse constructions, mutually reverse, indirectly reverse, ingressive, active-nonobjective. Shades of passivity were formed predominantly on the basis of pre-categorical constructions with the verbs “to be” / “to become” + participle II. In particular, in the corps of the ancient Saxon “Savior” there were a large number of non-copulative (free) structures with participle II, which could express passive or partiallypassive value. The author also notes that in addition to the typological distribution of the category of voice in the context of the opposition, “active-passive-reflexive”, in the Old Saxon paradigm of the category of voice there were observed subjective-objective relations, which in their turn had varieties: transformative, creative, addressive, factual, perceptual, emotional, instrumental.

A categorical framework for finite state machines

We provide a consistent way of looking at a range of finite state machines and their algebraic models. Our claim is that the natural representation of transitions of finite state machines is in terms of monoid homomorphisms, and distinct generalisation processes that can be applied to finite state machines correspond to distinct categorical generalisation processes at the level of the algebraic models.The generalisations we consider are those from deterministic to non-deterministic machines, from one-way to two-way machines, and from read-only machines to read/write machines. Hence the finite state machines we consider, and provide algebraic models for, are (deterministic and non-deterministic) finite state automata, two-way automata, Mealy machines, and bounded Turing machines.The categorical constructions corresponding to these generalisation processes are, respectively: altering the base category from functions to relations, applying the Geometry of Interaction, or Int construction, and a categorical process, which we refer to as the Comp construction, that uses the tensor on monoidal categories to construct graded categories.

Categorical constructions in C*-algebra theory

The notions of limits and colimits are studied in the category of C*-algebras. It is shown that limits and colimits of diagrams of C*-algebras are stable under tensor product by a fixed C*-algebra, and crossed product by a locally compact group.