The Isbell monad

In 1966, John Isbell introduced a construction on categories which he termed the "couple category" but which has since come to be known as the Isbell envelope. The Isbell envelope, which combines the ideas of contravariant and covariant presheaves, has found applications in category theory, logic, and differential geometry. We clarify its meaning by exhibiting the assignation sending a locally small category to its Isbell envelope as the action on objects of a pseudomonad on the 2-category of locally small categories; this is the Isbell monad of the title. We characterise the pseudoalgebras of the Isbell monad as categories equipped with a cylinder factorisation system; this notion, which appears to be new, is an extension of Freyd and Kelly's notion of factorisation system from orthogonal classes of arrows to orthogonal classes of cocones and cones.Comment: 21 page

Finding common ground: when the hippie counterculture immigrated to a rural redwood community

Youth of the 1960s took a collective stand against the establishment, challenging hegemonic forces intent on turning an informed citizenry into mere consumers; hypocrisy from the highest levels of government (Harrington 1962) was challenged by students, college enrollment was unprecedented (Roszak 1968). Unable to cause change at the top, scores of young people dropped out of mainstream culture in search of a better way to live (Miller 1991). Back-to-the-landers are the surviving members of the counterculture movement (Jacob 1997). Different from Sixties\u27 political radicals or utopian commune hippies, the back-to-the-land movement is evidence of counterculture success and provides an ideological model for community building. A hamlet in northern California is a model in community building because it exhibits the essential qualities of a resilient community: social cohesion, participatory decision-making, and shared commitment to environmental integrity (Theobald 1991). Immigrant generated conflict prevailed there during the early 1970s, based on fear. Serendipitously, residents created relationships and discovered common ground (Lamphere 1992). Smith and Krannich confirm, given an opportunity, newcomers and old-timers will discover they have more in common than previously believed (2009). Community members acknowledged their shared values, what Sumner terms the civil commons (2005); they established a unique kind of communitas of people and place (Turner 1969), sustained by frequent experiences of collective effervescence (Durkheim 1912) at events supporting both common and individual interests. Born in 1960, my life began with the counterculture. A consequence of free love, my hippie parents divorced in 1969; my mother, with four daughters, joined the back-to-the-land movement. Personal experience transforms this ethnography into autoethnography (Ellis and Bochner 2000). During a year of participant observation fieldwork (Spradley 1980), I returned to the town where I came of age as a hippie kid to discover how the people established peace

Continuum of Education Provision for Children with Special Educational Needs: Review of International Policies and Practices

The National Council for Special Education (NCSE) commissioned this research to create a descriptive map of international research which explores the notion of the continuum of education provision for children with special educational needs. It also aimed to determine and examine the nature of how the continuum of provision is conceptualised, operationalised and enacted in a sample of selected countries. Finally, it was to compare other countries and jurisdictions with existing provision and policy in Ireland and, in the context of an inclusive education as enshrined within the EPSEN Act (2004), identify implications for the development of provision in Ireland. The findings suggest reconceptualisation of the continuum as a community of provision, the redefinition of special educational needs in Ireland and the development of: • posts to build links within services and between services and service users. • simple, formal agreements between services. • staff understanding and collaboration between schools. • different staffing arrangements within the classroom, so as to create opportunities for new collaborative partnerships. • initial teacher training and ongoing professional development. • new models of assessment which remove the need for categories and formal health assessments and place the emphasis upon educational assessment of need. • a focus upon the class in resource allocation and deployment

ISCHE 42 - Looking from Above and Below:Rethinking the Social in the History of Education – Book of Abstracts

ISCHE 42 was conducted as a virtual conference due to the covid-19 pandemic. In adapting to this situation, the conference period was extended to two weeks, June 14-25, 2021, with a preconference on June 11, 2021. The abstracts for this conference are compiled in this volume