We propose an adjunction-based analysis of comparative (and similar) constructions that captures the morphological and semantic relation between comparative heads (e.g., -er, as) and comparative clauses (e.g., those headed by than or as). Primarily motivating this proposal are the syntactic similarities that we observe between comparative constructions and other adjunction structures in grammar...

We generalize the adjoint logics of Benton and Wadler (1996) and Reed (2009) to allow multiple different adjunctions between the same categories. This provides insight into the structural proof theory of cohesive homotopy type theory, which integrates the synthetic homotopy theory of homotopy type theory with the synthetic topology of Lawvere’s axiomatic cohesion. Reed’s calculus is parametrize...

Adjuncts are characteristically optional, but many, such as adverbs and adjectives, are strictly ordered. In Minimalist Grammars (MGs), it is straightforward to account for optionality or ordering, but not both. I present an extension of MGs, MGs with Adjunction, which accounts for optionality and ordering simply by keeping track of two pieces of information at once: the original category of th...

We prove new adjunction inequalities for embedded surfaces in fourmanifolds with non-negative self-intersection number using the Donaldson invariants. These formulas are completely analogous to the ones obtained by Ozsváth and Szabó [11] using the Seiberg-Witten invariants. To prove these relations, we give a fairly explicit description of the structure of the Fukaya-Floer homology of a surface...

For modules over a ring there is an adjunction between the associated sheaf functor AMod −→ Mod(SpecA) and the global sections functor Mod(SpecA) −→ AMod. In this note we develop the graded version of this result. All of this material is taken from EGA.

An algorithm of phrase structure building is proposed within the bare phrase structure framework. The algorithm is rooted in the idea that applications of Merge -the operation that combines syntactic objects -should not change the set of basic relations (in particular, c-command) in the existing structure, what Chomsky (2000) terms 'Least Tampering'. Under the proposed algorithm, this idea tran...