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Showing 1 to 4 of 4 for “"internal categories"”.
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Internal factorisation systems
We introduce internal factorisation systems for internal categories. We recall the definitions and theory of internal categories and factorisation systems. We develop a diagrammatic calculus of pullbacks for ease of internal calculation. To define an internal factorisation system we define and …
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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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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 …
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Monadic and Higher-Order Structure
… well as those in the literature for enriched and internal categories, then follow as corollaries of a general theory.