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Stream: theory: category theory

Topic: Lax twisted arrow categories

Eigil Rischel (Jun 30 2020 at 11:51):

Is there a good reference about basic properties of "lax twisted arrow categories"?
I am thinking about the following construction: given a 2-category $\mathcal{C}$ (strict or not), we can cook up a new 2-category $Tw^{lax}(\mathcal{C})$ where

• Objects are morphisms $f: x \to y$ in $\mathcal{C}$
• A map $(f: x \to y) \to (g: a \to b)$ consists of maps $i:x \to a, j: b \to y$ along with a not necessarily invertible 2-cell $jgi \Rightarrow f$.
• The 2-cells are defined in a natural way in terms of the 2-cells of $\mathcal{C}$.

It's not that the basic definition is absurdly complicated, but I'm hoping somebody has already worked out the basic properties of these guys.