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cronokirby.com | ||
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johnbender.us
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| | | | | Writings on computer stuff. | |
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thehousecarpenter.wordpress.com
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| | | | | A natural transformation is an operation on a category, or more precisely a family of operations, one for each object in the category, which is preserved by morphisms in the category. Each operation in the family is associated with a specific object $latex A$ in the category, which it is said to be on. The... | |
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bartoszmilewski.com
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| | | | | This is part 12 of Categories for Programmers. Previously: Declarative Programming. See the Table of Contents. It seems like in category theory everything is related to everything and everything can be viewed from many angles. Take for instance the universal construction of the product. Now that we know more about functors and natural transformations, can... | |
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math.andrej.com
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| | | [AI summary] The discussion revolves around the philosophical and methodological pluralism in mathematics, emphasizing that mathematics is a human-made construct with historical developments rather than an absolute, universal truth. Key points include the idea that different mathematical frameworks (e.g., classical vs. intuitionistic logic, paraconsistent logic) represent distinct 'worlds' of mathematics, each with its own standards and validity. The conversation highlights the importance of acknowledging these pluralistic perspectives without assuming a single, unifying foundation. It also touches on the role of context, the evolution of mathematical concepts, and the implications of relativism for the future of mathematics. The discussion underscores that ... | ||
