coconcept = concept

coconcept = concept

[Posina Venkata Rayudu]

[-- Attachment #1: Type: text/plain, Size: 2284 bytes --]

Dear All,

I wish you and your family a Happy Easter :)

In a festive spirit of Easter (somewhat dual to Christmas lectures
[presumably of answers]), I have an Easter question:

Having learned that (i) coproducts are isomorphic to products in
linear categories (zero object: 1 = 0;
https://lawverearchives.com/wp-content/uploads/2024/12/1992-categories-of-space-and-quantity.pdf<https://url.au.m.mimecastprotect.com/s/wqg4CD1vRkC5X7ZmXFAiYcj8wVb?domain=lawverearchives.com>,
p. 17), and (ii) pieces = points is the defining condition of quality
type (https://lawverearchives.com/wp-content/uploads/2025/01/2007-Axiomatic-cohesion.pdf<https://url.au.m.mimecastprotect.com/s/2qj6CE8wlRC3BwjGBuPs7c7HRCD?domain=lawverearchives.com>,
p.43), I added a few mundane ones such as the circle resulting from
coincidence of the two endpoints of a straight line segment, dynamical
systems resulting from codomain = domain, and isomorphisms resulting
from a map being being both epi and mono. Given that existence of
limits and colimits is of immense significance in category theory,
along with attendant arrow reversal in going from a concept to its
coconcept (and vice-versa; although reversing the arrows in the
definition of product gives the definition of sum, unlike the
definition of product that can be used to calculate products, sums can
only be verified based on the definition of sum, cf. co-element;
Lawvere & Rosebrugh, Sets for Mathematics, pp. 127-128), I'd be
grateful to you for any pointers you may have regarding the general
significance (conditions for and consequences) of: colimit = limit.

Thanking you,
Yours respectfully,
posina


You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message.

View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=files&GuestId=4eb9b40c-9b3a-48a5-9781-836e5a171e8b>   |   Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=4eb9b40c-9b3a-48a5-9781-836e5a171e8b>   |   Learn more about Microsoft 365 Groups<https://aka.ms/o365g>


[-- Attachment #2: Type: text/html, Size: 4232 bytes --]