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Stream: theory: category theory

Topic: "lax" composition?

Shea Levy (Oct 20 2020 at 13:55):

Is there a well-known concept that weakens categories by allowing composition to be "lax", i.e. we can (naturally in each component) go from $(f_{1}^{1} \circ ... \circ f_{1}^{k_1}) \circ ... \circ (f_{n}^{1} \circ ... \circ f_{n}^{k_n})$ to $f_{1}^{1} \circ ... \circ f_{1}^{k_1} \circ ... \circ f_{n}^{1} \circ ... \circ f_{n}^{k_n}$ , but not necessarily back?

Nathanael Arkor (Oct 20 2020 at 14:13):

Leinster gives a definition of (unbiased) lax bicategory in Definition 3.4.1 of Higher Operads, Higher Categories.