nLab Francis Borceux

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

• Mathematics Genealogy page

Writings

On category theory, and categorical algebra:

• Handbook of Categorical Algebra

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)

Further:

• F. Borceux, George Janelidze, Galois theories, Cambridge Studies in Advanced Mathematics 72

• 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

Introduction to topos theory:

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

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

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)

category: people