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Showing 1 to 6 of 6 for “"enriched categories"”.
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Internal enriched categories
… introduces and develops the theory of internal enriched categories, arising from the internalization of the theory of enriched categories. Given an internal monoidal category V in an ambient category E, we define the notions of V-enriched category, functor and natural transformation. We then …
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Topics in 2-categorical Algebra
In this thesis we will examine 2-categories and higher categorical structures and formulate 1-categorical theorems in the language of higher categories as well as formulate some internal definitions of these base structures in finitely complete categories. We will begin by defining the relevant 2- …
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Autonomous Pseudomonoids
… of autonomous pseudomonoids in monoidal bicategories. Autonomous pseudomonoids were introduced in [13] as generalisations of both autonomous monoidal categories and Hopf algebras. Much of the theory of autonomous pseudomonoids developed in [13] was inspired by the example of autonomous …
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Weakly enriched higher categories
… to begin to lay the foundations for a theory of enriched [infinity]categories. We introduce a definition of such objects, based on a non-symmetric version of Lurie's theory of [infinity]-operads. Our first main result is a construction of the correct homotopy theory of enriched …
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FROM DG-CATEGORIES OVER K TO K-LINEAR STABLE INFINITY-CATEGORIES
… that “idempotent- complete pretriangulated dg-categories over k are stable k-linear idempotent com- plete ∞-categories”. This result is a meeting point between algebraic topology and algebraic geometry. In 2013 L. Cohn proved it in a preprint, and in 2016, he updated the preprint to its latest …
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Loop Spaces and Iterated Higher Dimensional Enrichment
… has as a partial goal that of understanding the categories and functors that correspond to loop spaces and their associated topological functors. Progress towards this goal has been advanced greatly by the recent work of Balteanu, Fiedorowicz, Schwänzl, and Vogt who show a direct correspondence …