2-categories and cyclic homology

The topic of this thesis is the application of distributive laws between comonads to the theory of cyclic homology. The work herein is based on the three papers 'Cyclic homology arising from adjunctions', 'Factorisations of distributive laws', and 'Hochschild homology, lax codescent,and duplicial structure', to which the current author has contributed. Explicitly, our main aims are: 1) To study how the cyclic homology of associative algebras and of Hopf algebras in the original sense of Connes and Moscovici arises from a distributive law, and to clarify the role of different notions of bimonad in this generalisation. 2) To extend the procedure of twisting the cyclic homology of a unital associative algebra to any duplicial object defined by a distributive law. 3) To study the universality of Bohm and Stefan’s approach to constructing duplicial objects, which we do in terms of a 2-categorical generalisation of Hochschild (co)homology. 4) To characterise those categories whose nerve admits a duplicial structure.

Breaking old and new ground: a comparative study of coastal and inland naming in Berwickshire

This thesis investigates the place-names of four parishes in Berwickshire and compares coastal and inland naming patterns. Berwickshire is a large county that borders on northern England and historically formed part of Anglo-Saxon Northumbria. Partly due to the survival of extensive archives from the medieval priory of Coldingham, preserved in Durham Cathedral Archives, this county holds some of Scotland’s earliest recorded place- names. The parishes that form the research area are grouped together in the north-east of the county. Two of these parishes, Abbey St Bathans and Bunkle & Preston, are inland, and two, Cockburnspath and Coldingham, have extensive coastlines. The diversity of this group of parishes allows a comparative study of the place-names of coastal and inland areas to be undertaken. The topography of Berwickshire’s thirty-two parishes is very varied, and the four parishes have been chosen to reflect this range of landscapes. The place-names within the four parishes examined in this thesis derive almost exclusively from Old English, Older Scots, Modern Scots including Standard Scottish English, with a small minority derived from Old Norse, Gaelic, and Brittonic. The chronology of Old English, Older Scots, and Modern Scots is defined as given in the Concise Scots Dictionary: Old English is the period up to 1100, Older Scots is the period 1100-1700, and Modern Scots is the period 1700 onwards (CSD, 1985: xiii). Often with place-names it is not possible to give a precise dating for the coining of a toponym. For the purposes of this study, the language label given for a toponym is that of the date of the earliest record of the place-name with earlier linguistic evidence supplementing discussion. This thesis focuses on the names of topographic features, for example hills, rocks and woodland, and the role of perception in their naming. In order to compare the role of perception in inland and coastal naming, this thesis includes a diachronic study of the toponymy of the research area, along with two case studies. The first of these is a study of the toponymy of relief features, which focuses on generic elements in order to compare the perception of one type of referent in the two environments. The second is a study of the ‘colour’ category, which focuses on qualifying elements in order to compare the use of colour terms in the two environments. This thesis is the first comparative study of inland and coastal place-names, and it is one of the first to investigate new ways of using fieldwork as a central part of its methodology. In doing so it proposes innovative and nuanced ways to understand the toponymy of diverse landscapes within a community.