Qn 2. (a) State the definition of a terminal object in a category C. [2] (b)...

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Qn 2. (a) State the definition of a terminal object in a category C. [2] (b) Consider the category Metr of metric spaces and continuous maps. State with reasons whether or not the discrete metric space is a terminal object in Metr. [First recall the definition of the discrete metric]. [10] (c) Recall the category Matr whose objects are positive natural numbers, and arrows are m x n matrices with real-number entries. State with reasons whether or not 1 € N is a terminal object in this category. [7] Qn 2. (a) State the definition of a terminal object in a category C. [2] (b) Consider the category Metr of metric spaces and continuous maps. State with reasons whether or not the discrete metric space is a terminal object in Metr. [First recall the definition of the discrete metric]. [10] (c) Recall the category Matr whose objects are positive natural numbers, and arrows are m x n matrices with real-number entries. State with reasons whether or not 1 € N is a terminal object in this category. [7]

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a A terminal object in a category C is an object T in C such that for every object X in C there is a unique morphism from X to T This means that given ... View the full answer