Categories, norms and weights

The well-known Lawvere category R of extended real positive numbers comes with a monoidal closed structure where the tensor product is the sum. But R has another such structure, given by multiplication, which is *-autonomous. Normed sets, with a norm in R, inherit thus two symmetric monoidal closed structures, and categories enriched on one of them have a 'subadditive' or 'submultiplicative' norm, respectively. Typically, the first case occurs when the norm expresses a cost, the second with Lipschitz norms. This paper is a preparation for a sequel, devoted to 'weighted algebraic topology', an enrichment of directed algebraic topology. The structure of R, and its extension to the complex projective line, might be a first step in abstracting a notion of algebra of weights, linked with physical measures.Comment: Revised version, 16 pages. Some minor correction

The Return of Quarantinism and How to Keep It in Check: From Wishful Regulations to Political Accountability

Concerns about emerging and re-emerging infectious diseases have given a new lease of life to quarantinist measures: a series of time-honoured techniques for controlling the spread of infectious diseases through breaking the chain of human contagion. Since such measures typically infringe individual rights or privacy their use is subject to legal regulations and gives rise to ethical and political worries and suspicions. Yet in some circumstances they can be very effective. After considering some case studies that show how epidemics are unique, fluid and affected by a multitude of contingent factors, it is argued that the legal and ethical guidelines may not always be the best approach to discipline the use of quarantinist measures. An alternative model based on ex-post political accountability for reasonableness is proposed. This model restores the centrality of political decision and expert judgement in situations characterized by high risk, uncertainty and contingency. It is argued that such alternative model affords quicker and more flexible responses to serious outbreaks of infections, while providing adequate protection against abuses

A convenient category of locally preordered spaces

As a practical foundation for a homotopy theory of abstract spacetime, we extend a category of certain compact partially ordered spaces to a convenient category of locally preordered spaces. In particular, we show that our new category is Cartesian closed and that the forgetful functor to the category of compactly generated spaces creates all limits and colimits.Comment: 26 pages, 0 figures, partially presented at GETCO 2005; changes: claim of Prop. 5.11 weakened to finite case and proof changed due to problems with proof of Lemma 3.26, now removed; Eg. 2.7, statement before Lem. 2.11, typos, and other minor problems corrected throughout; extensive rewording; proof of Lem. 3.31, now 3.30, adde

Finite Sets And Symmetric Simplicial Sets

The category of finite cardinals (or, equivalently, of finite sets) is the symmetric analogue of the category of finite ordinals, and the ground category of a relevant category of presheaves, the augmented symmetric simplicial sets. We prove here that this ground category has characterisations similar to the classical ones for the category of finite ordinals, by the existence of a universal symmetric monoid, or by generators and relations. The latter provides a definition of symmetric simplicial sets by faces, degeneracies and transpositions, under suitable relations

Hubungan Keluarga dan Lingkungan Sosial dengan Prestasi Akademik Siswa Kelas VII di SMP Negeri 3 Babat Lamongan

Penelitian ini bertujuan untuk mengetahui hubungan keluarga dan lingkungan sosial dengan prestasi akademik siswa kelas VII di SMP Negeri 3 Babat Lamongan. Penelitian ini menggunakan kuantitatif dengan jenis korelasi sederhana yang dilakukan menggunakan bantuan SPSS.16. Subjek dalam penelitian ini adalah semua siswa kelas VII yang berjumlah 120 siswa. Analisis data penelitian ini menggunakan statistik parametrik dengan analisis regresi. Hasil analisis data menunjukkan bahwa ada hubungan yang signifikan antara keluarga dan lingkungan sosial dengan prestasi akademik siswa dengan melihat uji korelasi ganda yaitu harga F empirik lebih besar dibanding harga F teoritis pada taraf 5%. Dengan nilai F empirik 5,25 dan harga F teoritis sebesar 3,07 pada taraf 5%. Dengan demikian Ha diterima dan Ho ditolak, maka dapat disimpulkan bahwa ada hubungan antara keluarga dan lingkungan sosial dengan prestasi akademik siswa kelas VII di SMP Negeri 3 Babat Lamongan. Implikasi penelitian adalah peran keluarga dalam menunjang peningkatan kulitas pendidikan anak saat ini memang sangat dibutuhkan, pada keadaan nyata saat ini yang menyangkut peran keluarga terhadap peningkatan ataupun penurunan kualitas pendidikan banyak sekali.   Kata kunci : Keluarga, Lingkungan Sosial dan Prestasi Akademik&nbsp