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I am interested in knowing how we can use the concepts of Limits and Colimits in modeling problems in every day life? Could anyone provide (Software) engineering examples, perhaps? Or describe intuitively in general for what sorts of modeling problems we can use these concepts? (Providing even few examples will help in gaining an intuitive sense to generalize the application of the concepts in also other problems which may be of interest). Thank you.

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    $\begingroup$ Since this community seems to dislike the question, you could try at cstheory.stackexchange.com , where you are more likely to get good answers to a question like this. $\endgroup$
    – Andrej Bauer
    Commented Jan 12, 2014 at 17:31
  • $\begingroup$ Thank you, but the reason why I asked this question was that I was trying to learn category theory by myself and after studying a number of resources, it was still rather difficult for me to get an intuitive sense of the application of its concepts in my own discipline (software engineering). $\endgroup$
    – James
    Commented Jan 14, 2014 at 19:01
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    $\begingroup$ user221678: this question might be viable if you tighten it up. For a start, "everyday life" is much too broad: it sounds like you're asking for uses of category theory in going to the shops and feeding the cat. If you mean software engineering, say so specifically. Also, clarify whether you're talking about category theory in general or (co)limits in particular. (To me, it sounds odd to ask about just (co)limits.) If you asked "what are some applications of category theory to software engineering", with a bit of explanation, that might work as a big-list question. $\endgroup$
    – Tom Leinster
    Commented Jan 14, 2014 at 22:07
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    $\begingroup$ Let me just remind you that we encourage people to improve the questions so that they can be re-opened. $\endgroup$
    – Andrej Bauer
    Commented Jan 14, 2014 at 22:20
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    $\begingroup$ It seems strange to me that this question was closed as "too broad" while there is currently a question open asking for applications of sheaf theory to ring theory. I do not necessarily support the closing of that question, but point out that this question is significantly less broad than that other one. $\endgroup$
    – Jonathan Beardsley
    Commented Dec 22, 2015 at 15:36

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Here are some resources, not necessarily limited to limits and colimits:

  1. Since you specifically ask about software engineering, perhaps you can loko at Steve Easterbrooks's slides "An Introduction to Category Theory for Software Engineers" (which I found by using Google, have you tried?). In particular I draw your attention to slide 18.

  2. Databases and categories:

    • Easik by Robert Rosebrugh et al. lets you derive schemata in a categorical way, and in particular it uses limits and colimits to express various constructions in databases.
    • Spivak and Wisnesky's FQL is inspired by category theory also.

  3. More generally look at David Spivak's work on categories in informatics.

Let me give just one concrete example: a join of two tables in a relational database is pullback, which is a categorical limit. In general, whenever we combine two specifications subject to sharing constraints, that is a pullback.

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