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Weakly Terminal Objects in Quasicategories of \(\mathbb{SET}\) Endofunctors

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Abstract

The quasicategory ℚ of all set functors (i.e. endofunctors of the category \(\mathbb{SET}\) of all sets and mappings) and all natural transformations has a terminal object – the constant functor C1. We construct here the terminal (or at least the smallest weakly terminal object, which is rigid) in some important subquasicategories of ℚ – in the quasicategory \(\mathbb{F}\) of faithful connected set functors and all natural transformations, and in the quasicategories \(\mathbb{B}^{(\kappa)}\) of all set functors and natural transformations which preserve filters of points (up to cardinality κ).

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Authors and Affiliations

  1. Mathematical Institute of Charles University, Sokolovská 83, 186 75, Prague 8, Czech Republic

    Libor Barto

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  1. Libor Barto
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Correspondence to Libor Barto.

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Mathematics Subject Classifications (2000)

18A22, 18A25.

Libor Barto: This work was completed with the support of the Grant Agency of the Czech Republic under the grant 201/02/0148; supported also by MSM 113200007.

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Barto, L. Weakly Terminal Objects in Quasicategories of \(\mathbb{SET}\) Endofunctors. Appl Categor Struct 13, 257–264 (2005). https://doi.org/10.1007/s10485-005-5796-6

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  • DOI: https://doi.org/10.1007/s10485-005-5796-6

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