Proves equivalence of models of enhanced 2-sketches with algebras over enhanced 2-monads in locally presentable enhanced 2-categories, characterizing w-rigged limits and generalizing enriched orthogonality and monadicity results.
Enriched cofibration categories
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abstract
Cofibration categories are a formalization of homotopy theory useful for dealing with homotopy colimits that exist on the level of models as colimits of cofibrant diagrams. In this paper, we deal with their enriched version. Our main result claims that the category $[\mathcal{C},\mathcal{M}]$ of enriched diagrams equipped with the projective structure inherits a structure of a cofibration category whenever $\mathcal{C}$ is locally cofibrant (or, more generally, locally flat).
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math.CT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Enhanced $2$-categories of models of sketches as enhanced $2$-categories of algebras over monads
Proves equivalence of models of enhanced 2-sketches with algebras over enhanced 2-monads in locally presentable enhanced 2-categories, characterizing w-rigged limits and generalizing enriched orthogonality and monadicity results.