nLab Francis Borceux

Francis Borceux is a category theorist at Louvain (Belgium).

• Mathematics Genealogy page

Selected writings

Introducing the notion of weighted limits in enriched category theory:

• Francis Borceux, Une notion de $V$-limite, in Colloque sur l’algèbre des catégories. Amiens 1973. Résumés des conférences, Cahiers de topologie et géométrie différentielle 14 2 (1973) 153-223 [numdam:CTGDC_1973__14_2_153_0]

• Francis Borceux, Gregory Maxwell Kelly, A notion of limit for enriched categories, Bulletin of the Australian Mathematical Society 12 1 (1975) 49-72 [doi:10.1017/S0004972700023637]

On monadicity theorems:

• Francis Borceux, Brian Day, A monadicity theorem, Bulletin of the Australian Mathematical Society 17 2 (1977) 291-296 [doi:10.1017/S0004972700010480]

On algebra internal to a localic topos:

• Francis Borceux, Gilberte Van den Bossche, Algebra in a localic topos with applications to ring theory, Lecture Notes in Mathematics 1038, Springer 1983, ix+240 pp. MR85h:18005

On category theory, and categorical algebra:

• Handbook of Categorical Algebra (1994)

On nonabelian homological algebra, such as its diagram chasing lemmas, in Mal'cev categories, protomodular categories, semi-abelian categories and homological categories:

On accessible categories and sketches in the generality of enriched category theory:

• Francis Borceux, Carmen Quinteriro, Enriched accessible categories, Bull. Austral. Math. Soc. 54 (1996) 489-501 [doi:10.1017/S0004972700021900]

• Francis Borceux, Carmen Quinteriro, Jiří Rosický, A theory of enriched sketches, Theory and Applications of Categories, 4 3 (1998) 47-72 [tac:4-03, pdf]

On Galois theory:

• Francis Borceux, George Janelidze: Galois Theories, Cambridge Studies in Advanced Mathematics 72, Cambridge University Press (2001) [doi:10.1017/CBO9780511619939]

On accessible categories via doctrines of limits:

• Jiří Adámek, Francis Borceux, Stephen Lack, Jiri Rosicky, A classification of accessible categories, Journal of Pure and Applied Algebra 175 1–3 (2002) 7-30 [doi:10.1016/S0022-4049(02)00126-3]

On nonabelian homological algebra, such as its diagram chasing lemmas, in Mal'cev categories, protomodular categories, semi-abelian categories and homological categories:

• Francis Borceux, Dominique Bourn, Mal'cev, protomodular, homological and semi-abelian categories, Mathematics and Its Applications 566, Kluwer 2004 (doi:10.1007/978-1-4020-1962-3)

On monoid objects in monoidal categories:

• Francis Borceux, George Janelidze, Gregory Maxwell Kelly, Internal object actions, Commentationes Mathematicae Universitatis Carolinae (2005) Volume: 46, Issue: 2, page 235-255 (dml:249553)

Introduction to topos theory:

• Francis Borceux, Some glances at topos theory, lecture notes, Como (2018) [pdf, pdf, video playlist]

Presenting a pretorsion theory on Cat whose torsion(-free) objects are the groupoids (skeletal categories, respectively), hence whose “trivial objects” are the skeletal groupoids:

• Francis Borceux, Federico Campanini, Marino Gran, Walter Tholen, Groupoids and skeletal categories form a pretorsion theory in $Cat$ [arXiv:2207.08487]

Some other papers

• F. Borceux, I. Stubbe, A short introduction to enriched categories, pdf

• Francis Borceux, Gilberte Van Den Bossche, Recovering a frame from its sheaves of algebras, Journal of Pure and Applied Algebra 28, 2, May 1983, 141-154, doi

• Francis Borceux, On algebraic localizations, MR84c:18007, in Category theory (Gummersbach, 1981), pp. 13–22, Lecture Notes in Math. 962, Springer 1982.

That paper in the LNM Gummersbach volume has only short sketches of proofs. There is a larger French preprint version with full proofs:

• Francis Borceux, Sur les localisations algébriques, Preprint, Rapp. Sém. Math. Pures, Univ. Louvain, Louvain, Belgium, 1981

category: people