Abstract
This paper is a contribution to the theory of functor slices of J. Sichler and V. Trnková. For every ordinal α we introduce a basket \(\mathbb{E}_{\alpha}\), prove that every essentially algebraic category of height α is a slice of \(\mathbb{E}_{\alpha}\), characterize small slices of \(\mathbb{E}_{\alpha}\) and give a common generalization of known results about slices of the algebraic basket \(\mathbb{A}\).
Similar content being viewed by others
References
Adámek, J., Herrlich, H., Strecker, G.E.: Abstract and Concrete Categories. John Wiley and Sons, New York (1990)
Adámek, J., Rosický, J.: Locally Presentable and Accessible Categories. Cambridge University Press, Cambridge (1994)
Dalalyan, S., Petrosyan, A.: The slice classification of categories of coalgebras for comonads. Algebra Universalis 41, 177–185 (1999)
Isbell, J.R.: Epimorphisms and dominions. In: Eilenberg, S., et al. (eds.) Proc. Conference on Categorical Algebra (La Jolla, 1965), pp. 232–246. Springer, Berlin (1966)
Isbell, J.R.: Epimorphisms and dominions III. Amer. J. Math. 90, 1025–1030 (1968)
Jech, T.: Set Theory, 3rd edn. Springer-Verlag, Berlin (2003)
Koubek, V., Sichler, J., Trnková, V.: Algebraic functor slices. J. Pure Appl. Algebra 78, 275–290 (1992)
Reiterman, J.: Concrete full embeddings into categories of algebras and coalgebras. J. Pure Appl. Algebra 92, 173–184 (1994)
Sichler, J., Trnková, V.: Functor slices and simultaneous representations. In: Kaiser, H.K., Dorninger, D., Eigenthaler, G., Müller, W.B. (eds.) Contributions to General Algebra, vol. 7, pp. 299–320. Holder-Pichler-Tempsky, Wien (1991)
Trnková, V.: Functorial selection of morphisms. Canad. Math. Soc. Conf. Proc. 13, 435–447 (1992)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Barto, L. Slices of Essentially Algebraic Categories. Appl Categor Struct 17, 119–152 (2009). https://doi.org/10.1007/s10485-008-9150-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10485-008-9150-7