/sci/ - What are your favorite natural transformations and - Science & Math


08/21/20	New boards added: /vrpg/, /vmg/, /vst/ and /vm/
05/04/17	New trial board added: /bant/ - International/Random
10/04/16	New board for 4chan Pass users: /vip/ - Very Important Posts
[Hide] [Show All]

Anonymous
10/28/25(Tue)22:23:25 No.16830278

File: natural transformations.png (7 KB, 203x181)

7 KB PNG

Anonymous 10/28/25(Tue)22:23:25 No.16830278

What are your favorite natural transformations and adjoint functors?

Anonymous
10/29/25(Wed)00:04:26 No.16830326

Anonymous 10/29/25(Wed)00:04:26 No.16830326

>>16830278
Global sections and localization

Anonymous
10/29/25(Wed)00:20:29 No.16830337

Anonymous 10/29/25(Wed)00:20:29 No.16830337

>>16830326
how do you mean?

Anonymous
10/29/25(Wed)00:33:33 No.16830342

Anonymous 10/29/25(Wed)00:33:33 No.16830342

>>16830337
They are my favorite pair of adjoint functors.

Anonymous
10/29/25(Wed)01:02:16 No.16830352

Anonymous 10/29/25(Wed)01:02:16 No.16830352

>>16830342
what are these functors between?
(I've recently found that verifying naturality / adjointness is very relaxing, so I'm looking for fun examples to run through)

Anonymous
10/29/25(Wed)01:04:57 No.16830357

Anonymous 10/29/25(Wed)01:04:57 No.16830357

>>16830352
Quasi-coherent modules on a variety and modules over the ring of global sections.

Anonymous
10/29/25(Wed)01:07:24 No.16830360

Anonymous 10/29/25(Wed)01:07:24 No.16830360

File: tard.jpg (11 KB, 225x225)

11 KB JPG

>>16830357
mfw

Anonymous
10/29/25(Wed)05:03:04 No.16830446

Anonymous 10/29/25(Wed)05:03:04 No.16830446

File: IMG_4976.jpg (42 KB, 1280x720)

42 KB JPG

>>16830278
The determinant. You go through years of linear algebra having to deal with this seemingly arbitrary, but crucial concept, and then BAM.

Anonymous
10/29/25(Wed)05:18:42 No.16830452

Anonymous 10/29/25(Wed)05:18:42 No.16830452

>>16830446
Yeah that one's nice.

Anonymous
10/30/25(Thu)12:46:43 No.16831519

Anonymous 10/30/25(Thu)12:46:43 No.16831519

∀ and ∃ being the right and left adjoints of adding dummy variables

Name
Options
Comment
Verification	4chan Pass users can bypass this verification. [Learn More] [Login]
File
Please read the Rules and FAQ before posting. Additional supported file types are: PDF Use T_eX with [math] tags for inline and [eqn] tags for block equations. Right-click equations to view the source.

Janitor application acceptance emails are being sent out. Please remember to check your spam box!