130,944 research outputs found
Intrinsic Schreier-Mac Lane extension theorem II: The case of action accessible categories
No full textAbstractIn (Bourn, 2008 [11]), the Schreier-Mac Lane extension theorem in the category Gp of groups, which describes a simply transitive group action on a certain indexed class of non-abelian extensions, was extended to any exact pointed protomodular category with split extension classifiers. We show here that the same scheme of proofs allows us to extend it to any exact action accessible category in the sense of Bourn and Janelidze (2009) [13], which includes the case of any category of interest in the sense of Orzech (1972) [21]
The 3 × 3 lemma in the Σ-Mal'tsev and Σ-protomodular settings : Applications to monoids and quandles
No full textWe investigate what is remaining of the 3 × 3 lemma and of the denormalized 3 × 3 lemma, valid in a pointed protomodular and in a Mal'tsev category, respectively, in the context of partial pointed protomodular and partial Mal'tsev categories, relatively to a class Σ of points (i.e. of split epimorphisms with a fixed section). The results apply, among other structures, to monoids, semirings, and quandles
A NOTE ON THE CATEGORICAL NOTIONS OF NORMAL SUBOBJECT AND OF EQUIVALENCE CLASS
No full textIn a non-pointed category E, a subobject which is normal to an equivalence relation is not necessarily an equivalence class. We elaborate this categorical distinction, with a special attention to the Mal'tsev context. Moreover, we introduce the notion of fibrant equipment, and we use it to establish some conditions ensuring the uniqueness of an equivalence relation to which a given subobject is normal, and to give a description of such a relation
A note on the categorical notions of normal subobject and of equivalence class
No full textIn a non-pointed category E, a subobject which is normal to an equivalence relation is not necessarily an equivalence class. We elaborate this categorical distinction, with a special attention to the Mal’tsev context. Moreover, we introduce the notion of fibrant equipment, and we use it to establish some conditions ensuring the uniqueness of an equivalence relation to which a given subobject is normal, and to give a description of such a relation
CLOSEDNESS PROPERTIES OF INTERNAL RELATIONS II: BOURN LOCALIZATION
No full textWe say that a class D of categories is the Bourn localization of a class C of categories, and we write D =Loc(C), if D is the class of all (finitely complete) categories D such that for each object A in D, Pt(D↓A) ∈ C, where Pt(D ↓A) denotes the category of all pointed objects in the comma-category (D ↓A). As D. Bourn showed, if we take D to be the class of Mal’tsev categories in the sense of A. Carboni, J. Lambek, and M. C. Pedicchio, and C to be the class of unital categories in the sense of D. Bourn, which generalize pointed Jónsson-Tarski varieties, then D =Loc(C). A similar result was obtained by the author: if D is as above and C is the class of subtractive categories, which generalize pointed subtractive varieties in the sense of A. Ursini, then D =Loc(C). In the present paper we extend these results to abstract classes of categories obtained from classes of varieties. We also show that the Bourn localization of the union of the classes of unital and subtractive categories is still the class of Mal’tsev categories
Global Markets, Business Education and Ethical Dilemma's
No full textBrant, J Lines, D & Unwin, A (1998). Global Markets, Business Education and Ethical Dilemma's, in Bourn, D & Lambert (ed.) Global Perspectives in Initial Teacher Education: Training teachers for tomorrow, London: Development Education Association & Institute of Education pages 44-4
D. Allen, C. Bourn, J. Holyak (éd.), Accident Compensation after Pearson
No full textD. Allen, C. Bourn, J. Holyak (éd.), Accident Compensation after Pearson. In: Revue internationale de droit comparé. Vol. 32 N°2, Avril-juin 1980. pp. 457-459
D. Allen, C. Bourn, J. Holyak (éd.), Accident Compensation after Pearson
No full textD. Allen, C. Bourn, J. Holyak (éd.), Accident Compensation after Pearson. In: Revue internationale de droit comparé. Vol. 32 N°2, Avril-juin 1980. pp. 457-459
Watching reality weight loss TV. The effects on body satisfaction, mood, and snack food consumption
No full textAbstract not availableRebecca Bourn, Ivanka Prichard, Amanda D. Hutchinson, Carlene Wilso
Introduction
No full textthe text introduces the volume Pedagogy of hope by taking the title of a work by Freire. In particular, the concept of 'spearance' and its transformative significance in educational practice is critically examined
- …
