Maths - Category Theory - Sum




  sum arrow category  
generalisation   a kind of colimit
set example

sum set

disjoint union


group   free product
the free product for groups is generated by the set of all letters from a similar "almost disjoint" union where no two elements from different sets are allowed to commute.
Grp (abelian)  

direct sum
consists of the elements of the direct product which have only finitely many nonzero terms (this therefore coincides exactly with the direct product, in the case of finitely many factors)

the group generated by the "almost" disjoint union (disjoint union of all nonzero elements, together with a common zero)

vector space   direct sum
poset   least upper bound
base topological space   wedge


least upper bounds (joins)

Top   disjoint unions with their disjoint union topologies



When generating a sum for objects with structure then the structure associated with the link can be added to the sum object.

group sum category


product category construction

Products for groups are discussed on this page.


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see also:

Catsters youtube videos - Terminal and initial objects

Catsters youtube videos - Products and coproducts

Catsters youtube videos - Pullbacks and pushouts

Catsters youtube videos - General limits and colimits

Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

flag flag flag flag flag flag The Princeton Companion to Mathematics - This is a big book that attempts to give a wide overview of the whole of mathematics, inevitably there are many things missing, but it gives a good insight into the history, concepts, branches, theorems and wider perspective of mathematics. It is well written and, if you are interested in maths, this is the type of book where you can open a page at random and find something interesting to read. To some extent it can be used as a reference book, although it doesn't have tables of formula for trig functions and so on, but where it is most useful is when you want to read about various topics to find out which topics are interesting and relevant to you.


Terminology and Notation

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