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grossack.site | ||
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www.jeremykun.com
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| | | | | This post is mainly mathematical. We left it out of our introduction to categories for brevity, but we should lay these definitions down and some examples before continuing on to universal properties and doing more computation. The reader should feel free to skip this post and return to it later when the words "isomorphism," "monomorphism," and "epimorphism" come up again. Perhaps the most important part of this post is the description of an isomorphism. | |
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xorshammer.com
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| | | | | There is a class of all cardinalities $latex \mathbf{Card}$, and it has elements $latex 0$, $latex 1$ and operations $latex +$, $latex \cdot$, and so forth defined on it. Furthermore, there is a map $latex \mathrm{card}\colon\mathbf{Set}\to\mathbf{Card}$ which takes sets to cardinalities such that $latex \mathrm{card}(A\times B)=\mathrm{card}(A)\cdot\mathrm{card}(B)$ (and so on). Ordinary generating functions can be thought... | |
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bartoszmilewski.com
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| | | | | Previously: Topology as a Dietary Choice. Category theory lets us change the focus from individual objects to relationships between them. Since topology is defined using open sets, we'd start by concentrating on relations between sets. One such obvious relation is inclusion. It imposes a categorical structure on the subsets of a given set $latex X$.... | |
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tm.durusau.net
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