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Adjunction in the Absence of Identity

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Abstract

We develop a bicategorical setup in which one can speak about adjoint 1-morphisms even in the absence of genuine identity 1-morphisms. We also investigate which part of 2-representation theory of 2-categories extends to this new setup.

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Notes

  1. This also has to do with the terminology. There has been a suggestion that ‘weakly fiax’ should be ‘fax’ and ‘weakly fiat’ should be ‘fat’, which was dismissed by a majority of the authors of the current paper.

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Acknowledgements

This research was partially supported by the Swedish Research Council and Göran Gustafsson Stiftelse. We especially thank Marco Mackaay in conversation with whom the main idea behind this paper crystalized. We thank Gustavo Jasso for information about adjunction of semifunctors. We are grateful to the referee for very helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Uppsala University, Box. 480, SE-75106, Uppsala, Sweden

    Hankyung Ko & Volodymyr Mazorchuk

  2. Beijing Advanced Innovation Center for Imaging Theory and Technology, Academy for Multidisciplinary Studies, Capital Normal University, Beijing, 100048, China

    Xiaoting Zhang

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  1. Hankyung Ko
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  2. Volodymyr Mazorchuk
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  3. Xiaoting Zhang
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Correspondence to Xiaoting Zhang.

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Communicated by Nicola Gambino.

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Ko, H., Mazorchuk, V. & Zhang, X. Adjunction in the Absence of Identity. Appl Categor Struct 30, 123–172 (2022). https://doi.org/10.1007/s10485-021-09652-y

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