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Basic Concepts of Enriched Category Theory
- GenresMathematics
256 pages, Paperback
First published April 30, 1982
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May 21, 2023
I've read Categories for the Working Mathematician before, but this was what really got me into category theory. I found chapters 1 and 2 very technical, but after that it really picks up. Each chapter iterates on the concepts of the earlier ones refining and exemplifying them so that the whole book tells a very coherent story.
Not only is it a great introduction to enriched category theory, it also made me understand topics of ordinary category theory, it also made me understand it's topics in ordinary category theory which felt technical and unmotivated in Categories Work like ends, kan extensions and density.
The generalisation of conical to weighted limits enables the rather beautiful formalism and calculus of weighted limits. In the ordinary case these admit an intuitive interpretation similar to that of cones with the difference that there can be several arrows an object in the base to the vertex of the cone instead of a single unique arrow for each object. Similarly in the general case a cone is characterized by spaces of morphism between the objects in the base and between those and the vertex. This intuition is not mentioned in the book even though I think it is rather important. I suppose if I was less lazy I could have understood this sooner than years after initial learning the definition of weighted limits from this book, because it's kind of obvious, but I still wish it had been spelled out.
Not only is it a great introduction to enriched category theory, it also made me understand topics of ordinary category theory, it also made me understand it's topics in ordinary category theory which felt technical and unmotivated in Categories Work like ends, kan extensions and density.
The generalisation of conical to weighted limits enables the rather beautiful formalism and calculus of weighted limits. In the ordinary case these admit an intuitive interpretation similar to that of cones with the difference that there can be several arrows an object in the base to the vertex of the cone instead of a single unique arrow for each object. Similarly in the general case a cone is characterized by spaces of morphism between the objects in the base and between those and the vertex. This intuition is not mentioned in the book even though I think it is rather important. I suppose if I was less lazy I could have understood this sooner than years after initial learning the definition of weighted limits from this book, because it's kind of obvious, but I still wish it had been spelled out.
Displaying 1 of 1 review