This note analyzes in terms of categorial proof theory some standard assumptions about negation in the absence of any other connective. It is shown that the assumptions for an involutive negation, like classical negation, make a kind of adjoint situation, which is named involutive adjunction. The notion of involutive adjunction amounts in a precise sense to adjunction where an endofunctor is ad...

We categorify the adjunction between locales and topological spaces, this amounts to an (generalized) bounded ionads topoi. show that is idempotent. relate Scott adjunction, which was discussed from a more categorical point of view in [Liba]. hint $0$-dimensional inhabits categorified one.

Theorem 1.1. ([E]) Let X = B ∪ (1-handles) ∪ (2-handles) be four-dimensional handlebody with one 0-handle and no 3or 4-handles. Then • The standard symplectic structure on B can be extended over 1-handles so that manifold X1 = B 4 ∪ (1-handles) is a compact Stein domain. • If each 2-handle is attached to ∂X1 along a Legendrian knot with framing one less then Thurston-Bennequin framing of this k...

Hunter, T. (2010). Relating Movement and Adjunction in Syntax and Semantics. PhD thesis, University of Maryland. Hunter, T. (2011). Deconstructing merge and move to make room for adjunction. Ms., Yale University, available from http://www.ling.yale.edu/ ̃timh/. Lebeaux, D. (1988). Language acquisition and the form of the grammar. PhD thesis, University of Massachussetts, Amherst. Stabler, E. P. ...