publication . Preprint . Other literature type . 2011

Concrete fibrations

Pagnan, Ruggero;
Open Access English
  • Published: 24 May 2011 Journal: issn: 0029-4527, Copyright policy
  • Publisher: Duke University Press
As far as we know, no notion of concrete fibration is available. We provide one such notion in adherence to the foundational attitude that characterizes the adoption of the fibrational perspective in approaching fundamental subjects in category theory and discuss it in connection with the notion of concrete category and the notions of locally small and small fibrations. We also discuss the appropriateness of our notion of concrete fibration for fibrations of small maps, which is relevant to algebraic set theory.
free text keywords: 18A05, Mathematics - Category Theory, 18A15, 18B99, concrete fibration, Isbell condition
19 references, page 1 of 2

[1] Jiˇr´ı Ad´amek. Theory of mathematical structures. D. Reidel Publishing Co., Dordrecht, 1983.

[2] Jiˇr´ı Ad´amek, Horst Herrlich, and George E. Strecker. Abstract and concrete categories: the joy of cats. Repr. Theory Appl. Categ., (17):1-507, 2006. Reprint of the 1990 original [Wiley, New York; MR1051419].

[3] Jean B´enabou. Th´eories relatives `a un corpus. C. R. Acad. Sci. Paris S´er. A-B, 281(20):Ai, A831-A834, 1975.

[4] Jean B´enabou. Fibered categories and the foundations of naive category theory. J. Symbolic Logic, 50(1):10-37, 1985.

[5] Francis Borceux. Handbook of categorical algebra. 2, volume 51 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1994. Categories and structures.

[6] Samuel Eilenberg and Saunders MacLane. General theory of natural equivalences. Trans. Amer. Math. Soc., 58:231-294, 1945.

[7] A. Grothendieck. Cat´egories fibr´ees et descente (Expos´e vi). Lecture Notes in Mathematics, (224):145-194, 1970.

[8] J. R. Isbell. Two set-theoretical theorems in categories. Fund. Math., 53:43-49, 1963.

[9] Freyd Peter J. Concreteness. J. Pure Appl. Algebra, 3:171-191, 1973.

[10] Bart Jacobs. Categorical logic and type theory, volume 141 of Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam, 1999.

[11] P. T. Johnstone. Topos theory. Academic Press [Harcourt Brace Jovanovich Publishers], London, 1977. London Mathematical Society Monographs, Vol. 10.

[12] A. Joyal and I. Moerdijk. Algebraic set theory, volume 220 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1995.

[13] G. M. Kelly. A note on relations relative to a factorization system. In Category theory (Como, 1990), volume 1488 of Lecture Notes in Math., pages 249-261. Springer, Berlin, 1991.

[14] Aaron Klein. Relations in categories. Illinois J. Math., 14:536-550, 1970. [OpenAIRE]

[15] Saunders Mac Lane. Categories for the working mathematician, volume 5 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1998.

19 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Preprint . Other literature type . 2011

Concrete fibrations

Pagnan, Ruggero;