Adjunction in the absence of identity
Hankyung Ko, Volodymyr Mazorchuk, Xiaoting Zhang
TL;DR
This paper introduces a bicategorical framework allowing the discussion of adjoint morphisms without relying on identity morphisms, and explores how 2-representation theory extends to this novel context.
Contribution
It presents a new bicategorical setup for adjunctions without identity morphisms and analyzes its implications for 2-representation theory.
Findings
Extended adjunction concepts to non-identity contexts
Identified parts of 2-representation theory applicable in this setup
Provided foundational tools for further research in bicategories
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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Geometry