We prove that iteration theories can be introduced as algebras for the monad Rat on the category of signatures assigning to every signature Σ the rationalΣ-tree signature. This supports the result that iteration theories axiomatize precisely the equational properties of least fixed points in domain theory: Rat is the monad of free rational theories and every free rational theory has a continuou...

The well known isomorphism relating the rational algebraic K-theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map (the “Segre map”) of infinite loop spaces. Moreover, the associated Chern character map on rational homotopy groups is shown to be a ring isomorphism. A technique is introduced which establishe...

A theory of rationality is a theory that evaluates instances of reasoning as rational, irrational, or (ir)rational to some degree. Theories can be categorized as rule-based or consequentialist. Rule-based theories say that rational reasoning accords with certain rules (e.g., of logic or probability). Consequentialist theories say that rational reasoning tends to produce good consequences. For i...

Rational counterterms are a key ingredient for the automation of loop calculations through numerical methods. Building on recently established properties rational terms UV origin at two loops, in this paper we present systematic method determination within spontaneously broken theories. In particular introduce generalised vev-expansion approach that makes it possible to obtain theory by means u...

A bstract We systematically study how the integrality of conformal characters shapes space fermionic rational field theories in two dimensions. The suggests that on torus with a given choice spin structures should be invariant under principal congruence subgroup PSL(2 , ℤ). invariance strongly constrains possible values central charge as well weights both Neveu-Schwarz and Ramond sectors, which...