Results 11 to 20 of about 1,474,815 (298)
Internal enriched categories [PDF]
, 2019 This dissertation introduces and develops the theory of internal enriched categories, arising from the internalization of the theory of enriched categories.
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What is a categorical model of arrows? [PDF]
, 2011 We investigate what the correct categorical formulation of Hughes’ Arrows should be. It has long been folklore that Arrows, a functional programming construct, and Freyd categories, a categorical notion due to Power, Robinson and Thielecke, are somehow ...
Robert Atkey, Atkey, Robert
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Cartesian Differential Categories as Skew Enriched Categories [PDF]
Applied Categorical Structures, 2021 AbstractWe exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids—or in a straightforward generalisation, the category of modules over a commutative rigk. However, the tensor product on this category is not the usual one, but
Richard Garner, Jean-Simon Pacaud Lemay
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Enriched Categories of Coalgebras [PDF]
Electronic Journal of MathematicsJean-Paul Mavoungou
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Enriched locally generated categories
Theory and Applications of Categories, 2022 We introduce the notion of $\mathcal{M}$-locally generated category for a factorization system $(\mathcal{E},\mathcal{M})$ and study its properties. We offer a Gabriel-Ulmer duality for these categories, introducing the notion of nest. We develop this theory also from an enriched point of view.
Di Liberti, I. (Ivan), Rosický, J.
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Rectification of enriched ∞–categories [PDF]
Algebraic & Geometric Topology, 2015 We prove a rectification theorem for enriched1‐categories: if V is a nice monoidal model category, we show that the homotopy theory of1‐categories enriched in V is equivalent to the familiar homotopy theory of categories strictly enriched in V . It follows, for example, that1‐categories enriched in spectra or chain complexes are equivalent to spectral ...
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Duoidally Enriched Freyd Categories
, 2023 To appear at RAMiCS ...
Chris Heunen, Jesse Sigal
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Monoidal Categories Enriched in Braided Monoidal Categories [PDF]
International Mathematics Research Notices, 2017 AbstractWe introduce the notion of a monoidal category enriched in a braided monoidal category $\mathcal{V}$. We set up the basic theory, and prove a classification result in terms of braided oplax monoidal functors to the Drinfeld centre of some monoidal category $\mathcal{T}$.Even the basic theory is interesting; it shares many characteristics with ...
Morrison, Scott, Penneys, David
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Grothendieck Enriched Categories
Applied Categorical Structures, 2022 35 pages.
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Applied Categorical Structures, 2022 AbstractWe introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. Then, we contextualize the new notion by comparing it to another known generalization of enrichment: that of enrichment for indexed categories.
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