Bilimits are bifinal objects |
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| Affiliation: | 1. Institute of Mathematics, Czech Academy of Sciences, ?itná 25, 115 67 Praha 1, Czech Republic;2. Institut Galilée, Université Paris 13, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France;1. Sapientia Hungarian University of Transylvania, Târgu-Mure?/Corunca, Sighi?oarei road, nr. 2, Postal code: 540485, Romania;2. University of Wisconsin-Madison, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706, United States of America;1. Department of Mathematics, Swansea University, Swansea University Bay Campus, Fabian Way, Swansea SA1 8EN, UK;2. Faculty of Mathematics, University of Bia?ystok, K. Cio?kowskiego 1M, 15-245 Bia?ystok, Poland;3. Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK;4. Département de Mathématique, Université Libre de Bruxelles, Bd du Triomphe, B-1050 Brussels, Belgium;1. Department of Mathematics and Computer Science, Eindhoven University of Technology, De Groene Loper 5, 5612 AZ, Eindhoven, Netherlands;2. Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090, Wien, Austria;1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4L8, Canada;2. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom |
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| Abstract: | We prove that a (lax) bilimit of a 2-functor is characterized by the existence of a limiting contraction in the 2-category of (lax) cones over the diagram. We also investigate the notion of bifinal object and prove that a (lax) bilimit is a limiting bifinal object in the 2-category of (lax) cones. Everything is developed in the context of marked 2-categories, so that the machinery can be applied to different levels of laxity, including pseudo-limits. |
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| Keywords: | 18D30 18D70 18N10 |
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