Non-Pointed Strongly Protomodular Theories

Applied Categorical Structures - Tập 12 Số 4 - Trang 319-338 - 2004
Borceux, F.1
1Faculté des Sciences, Université Catholique de Louvain, Louvain-la-Neuve, Belgium. e-mail

Tóm tắt

We give criterions for strong protomodularity and prove that the strong protomodularity of an algebraic theory is inherited by its models in a category with finite limits. We give examples of strongly protomodular theories with several constants: C *-algebras, rings, Heyting algebras and Boolean algebras.

Tài liệu tham khảo

Borceux, F.: A Handbook of Categorical Algebra, Vols. I, II, Cambridge University Press, 1994. citation_title=Mal'cev, Protomodular, Homological and Semi-Abelian Categories; citation_publication_date=2004; citation_id=CR2; citation_author=F. Borceux; citation_author=D. Bourn; citation_publisher=Kluwer Academic Publisher Borceux, F. and Clementino, M. M.: Topological protomodular algebras (submitted for publication). Bourn, D.: Normalization equivalence, kernel equivalence and affine categories, in Lecture Notes in Math. 1448, Springer, 1991, pp. 43–62. citation_journal_title=Appl. Categ. Structures; citation_title=Mal'cev categories and fibrations of pointed objects; citation_author=D. Bourn; citation_volume=4; citation_publication_date=1996; citation_pages=302-327; citation_id=CR5 citation_journal_title=Theory Appl. Categ.; citation_title=Normal functors and strong protomodularity; citation_author=D. Bourn; citation_volume=7; citation_publication_date=2000; citation_pages=206-218; citation_id=CR6 Bourn, D.: Protomodular aspects of the dual of a topos, Adv. in Math. (to appear). citation_journal_title=Theory Appl. Categ.; citation_title=Centrality and normality in protomodular categories; citation_author=D. Bourn, M. Gran; citation_volume=9; citation_publication_date=2002; citation_pages=151-165; citation_id=CR8 citation_journal_title=Theory Appl. Categ.; citation_title=Protomodularity, descent and semi-direct products; citation_author=D. Bourn, G. Janelidze; citation_volume=4; citation_publication_date=1998; citation_pages=37-46; citation_id=CR9 citation_journal_title=Theory Appl. Categ.; citation_title=Characterization of protomodular varieties of universal algebra; citation_author=D. Bourn, G. Janelidze; citation_volume=11; citation_publication_date=2002; citation_pages=143-147; citation_id=CR10 citation_journal_title=Appl. Categ. Structures; citation_title=Some remarks on Maltsev and Goursat categories; citation_author=A. Carboni, G. M. Kelly, M. C. Pedicchio; citation_volume=1; citation_publication_date=1993; citation_pages=385-421; citation_id=CR11 citation_journal_title=Proc. Sympos. Pure Math.; citation_title=A categorical setting for the Baer extension theory; citation_author=M. Gerstenhaber; citation_volume=17; citation_publication_date=1970; citation_pages=50-64; citation_id=CR12 Gran, M. and Rosický , J.: Semi-Abelian monadic categories (submitted for publication). citation_journal_title=J. Pure Appl. Algebra; citation_title=Semi-Abelian categories; citation_author=G. Janelidze, L. Márki, W. Tholen; citation_volume=168; citation_publication_date=2002; citation_pages=367-386; citation_id=CR14 Johnstone, P. T.: Stone Spaces, Cambridge University Press, 1982. Johnstone, P. T.: Sketches of an Elephant: A Topos Theory Compendium, Vol. 1, Oxford University Press, 2002. Johnstone, P. T.: A note on the semiabelian variety of Heyting semilattices, Publications of the Fields Institute (to appear). Kelley, J.: General Topology, Springer, 1971 (from Van Nostrand, 1955). Manes, E.: A triple theoretic construction of compact algebras, in Lecture Notes in Math. 80, Springer, 1969, pp. 91–118. Rodelo, D.: Moore categories (submitted for publication).