On an adjoint functor to the Thom functor

Continuity is an Adjoint Functor

1. INTRODUCTION. The emergence of category theory, introduced by S. Eilen-berg and S. Mac Lane in the 1940s (cf. [2]), was among the most important mathematical developments of the twentieth century. The profound impact of the theory continues to this day, and categorical methods are currently used, for example, in algebra, geometry, topology, mathematical physics, logic, and theoretical comput...

On the Functor ℓ2

We study the functor `2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and both categories are enriched over algebraic domains. The functor preserves daggers, monoidal structures, enrichment, and various (co)limits, but has no adjoints. Up to unitaries, its direct image consists precisely of the partial isometries, but its ...

On the quadratic Fock functor

We prove that the quadratic second quantization of an operator p on L2(Rd)∩L∞(Rd) is an orthogonal projection on the quadratic Fock space if and only if p = MχI , where MχI is a multiplication operator by a characteristic function χI .

An Introduction to Predicate-functor Logic

The quadratic Fock functor

We construct the quadratic analogue of the boson Fock functor. While in the first order (linear) case all contractions on the 1–particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. The encouraging fact is that it contains, as proper subgroups (i.e. the contractions), all the gauge transformation...