1 июл. 2015 г. · A well-known example is the equivalence between groups and and one-object categories with all morphisms invertible (i.e. all morphisms are ...

26 авг. 2011 г. · The (∞,n)-category of bordisms is an important example for many reasons, the most imporant of which is its role in the Baez-Dolan cobordism hypothesis.

25 мар. 2010 г. · Objects and the relationships between them. · The use of functors to build bridges between different categories. · Breaking an object up into ...

14 апр. 2021 г. · The category of Hilbert spaces and bounded linear maps is pretty badly behaved: No limits, no colimits, not even (co)products.

11 мая 2022 г. · [cont'd] E.g. take Set to be the cat of sets, with hom-sets not artificially disjointified, i.e. morphisms are just functions f, not triples (X, ...

17 июн. 2020 г. · There are a lot of interesting and creative examples of categories, such as for example, the category whose objects are the positive integers.

22 окт. 2009 г. · Category theory just provides a language. Sometimes it provides really useful descriptions and metaphors and theorems, but most theorems can't be proved using ...

17 дек. 2012 г. · But perhaps what you want is what I used as an example to illustrate the concepts of Category Theory. (I call it the Toy Category).

12 апр. 2017 г. · If a category is complete in the ordinary sense and admits enriched powers, then it is complete in the enriched sense of admitting all weighted ...

14 дек. 2011 г. · Category theory gives an abundance of such categories: elementary toposes. They are a special class of cartesian closed categories. They ...