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| 2025-02-24 12:13:57 +0100 | <euouae> | but e.g. in the HoTT book in the Appendix the type universes are presented as U_1, U_2, ... and I think those are types, kinds, higher kinds, etc |
| 2025-02-24 12:13:51 +0100 | <ncf> | or do you mean universe levels? this is one of the choices you can make; you can have a MLTT with no universes, or one universe, or a countable hierarchy of universes, or crazier things |
| 2025-02-24 12:13:34 +0100 | <euouae> | I'm doing personal "research" so there's no fixed order/set of papers/articles I'm reading |
| 2025-02-24 12:13:03 +0100 | <ncf> | euouae: i think that might depend on how you present the syntax and what you mean by "order". i don't think the answer is very significant |
| 2025-02-24 12:10:45 +0100 | CiaoSen | (~Jura@2a02:8071:64e1:7180:4e50:ddff:fe9b:8922) (Ping timeout: 248 seconds) |
| 2025-02-24 12:09:51 +0100 | ethantwardy | (user@user/ethantwardy) (Ping timeout: 246 seconds) |
| 2025-02-24 12:08:49 +0100 | <euouae> | jackdk: thanks for the links, I will check them out. I can at least say I've seen the diagram of the first video before |
| 2025-02-24 12:08:27 +0100 | <euouae> | I don't quite grasp the significance of that. also last question I promise. thank you |
| 2025-02-24 12:08:11 +0100 | <euouae> | I know for the lambda cube only two sorts are used, types and kinds, say |
| 2025-02-24 12:07:43 +0100 | <euouae> | Does MLTT have sorts of order N? Or just 2? |
| 2025-02-24 12:06:21 +0100 | <ncf> | every model of MLTT is a locally cartesian closed category because that's the structure you need to interpret the basic features of a type theory; but the models may also have more structure to account for the other features |
| 2025-02-24 12:05:36 +0100 | <ncf> | they don't |
| 2025-02-24 12:03:02 +0100 | <euouae> | is it like a common core? |
| 2025-02-24 12:02:56 +0100 | <euouae> | Then how come they all have the same CCC models? |
| 2025-02-24 12:02:45 +0100 | <ncf> | multiple; there are several choices you can make and features you can add |
| 2025-02-24 12:00:20 +0100 | fp1 | fp |
| 2025-02-24 12:00:19 +0100 | fp | (~Thunderbi@130.233.70.89) (Ping timeout: 260 seconds) |
| 2025-02-24 12:00:14 +0100 | <euouae> | and is that a single theory or multiple? |
| 2025-02-24 12:00:01 +0100 | <ncf> | nlab usually means martin-löf type theory |
| 2025-02-24 11:59:42 +0100 | <euouae> | e.g. the lambda cube has several, not just CoC at the top |
| 2025-02-24 11:59:33 +0100 | <euouae> | I see. What is meant by dependent type theory? This is another naive question. I know what a dependent type is vaguely, but I don't think there's a single "theory", that's why I'm asking |
| 2025-02-24 11:58:41 +0100 | <ncf> | yes |
| 2025-02-24 11:57:52 +0100 | fp1 | (~Thunderbi@wireless-86-50-141-43.open.aalto.fi) fp |
| 2025-02-24 11:57:37 +0100 | <euouae> | I mean *those certain* categories that are specified |
| 2025-02-24 11:56:40 +0100 | <euouae> | ncf: when that link says categories provide the semantics, does it mean that categories are models for type theories? |
| 2025-02-24 11:56:29 +0100 | euleritian | (~euleritia@ip4d17fae8.dynamic.kabel-deutschland.de) |
| 2025-02-24 11:56:12 +0100 | euleritian | (~euleritia@dynamic-176-006-145-147.176.6.pool.telefonica.de) (Read error: Connection reset by peer) |
| 2025-02-24 11:55:45 +0100 | <jackdk> | I wouldn't worry about the meme words (but for completeness, the `...` is "monoid objects", and you need to specify the tensor; see https://www.youtube.com/watch?v=cB8DapKQz-I ) . I don't know the details, but you can represent lambda calculus terms in CCCs; see Conal Eliott's excellent work on "compiling to categories" at e.g. https://www.youtube.com/watch?v=4WMfKhKKVN4 https://www.youtube.com/watch?v=zooYfk5-yPY |
| 2025-02-24 11:55:12 +0100 | euleritian | (~euleritia@dynamic-176-006-145-147.176.6.pool.telefonica.de) |
| 2025-02-24 11:54:31 +0100 | euleritian | (~euleritia@ip4d17fae8.dynamic.kabel-deutschland.de) (Ping timeout: 244 seconds) |
| 2025-02-24 11:49:33 +0100 | <ncf> | i don't understand the question but see https://ncatlab.org/nlab/show/relation+between+type+theory+and+category+theory |
| 2025-02-24 11:48:57 +0100 | acidjnk | (~acidjnk@p200300d6e7283f50e1932e8352fc3c3c.dip0.t-ipconnect.de) (Ping timeout: 252 seconds) |
| 2025-02-24 11:46:14 +0100 | <euouae> | I vaguely have heard of something about cartesian-closed categories, but I'm not sure if they capture all the salient points. What is the idea then? How are functors to be understood in type theory if there is no categorical formulation of it? Or am I missing something? |
| 2025-02-24 11:45:17 +0100 | <euouae> | From my studies on type theory, e.g. the lambda cube, I can't seem to figure out how type theory (theories) is formalized on category theory. I'm not sure if it is known or not. |
| 2025-02-24 11:44:40 +0100 | <euouae> | Hello I've been thinking about statements such as 'monads are just ... in the category of endofunctors' (fill in blank for me because I don't know it exactly) |
| 2025-02-24 11:44:18 +0100 | euouae | (~euouae@user/euouae) euouae |
| 2025-02-24 11:43:57 +0100 | euleritian | (~euleritia@ip4d17fae8.dynamic.kabel-deutschland.de) |
| 2025-02-24 11:42:50 +0100 | euleritian | (~euleritia@dynamic-176-006-145-147.176.6.pool.telefonica.de) (Read error: Connection reset by peer) |
| 2025-02-24 11:38:32 +0100 | ash3en | (~Thunderbi@89.246.174.164) (Remote host closed the connection) |
| 2025-02-24 11:38:28 +0100 | ash3en | (~Thunderbi@89.246.174.164) ash3en |
| 2025-02-24 11:36:52 +0100 | alfiee | (~alfiee@user/alfiee) (Ping timeout: 252 seconds) |
| 2025-02-24 11:32:31 +0100 | alfiee | (~alfiee@user/alfiee) alfiee |
| 2025-02-24 11:22:32 +0100 | Tuplanolla | (~Tuplanoll@91-159-69-59.elisa-laajakaista.fi) Tuplanolla |
| 2025-02-24 11:16:44 +0100 | kuribas | (~user@2a02:1810:2825:6000:f4c8:b5d5:3a82:9bab) kuribas |
| 2025-02-24 11:13:19 +0100 | rvalue | (~rvalue@user/rvalue) rvalue |
| 2025-02-24 11:12:47 +0100 | rvalue | (~rvalue@user/rvalue) (Read error: Connection reset by peer) |
| 2025-02-24 11:01:59 +0100 | merijn | (~merijn@77.242.116.146) merijn |
| 2025-02-24 10:53:27 +0100 | fp | (~Thunderbi@130.233.70.89) fp |
| 2025-02-24 10:51:36 +0100 | lortabac | (~lortabac@2a01:e0a:541:b8f0:55ab:e185:7f81:54a4) (Quit: WeeChat 4.5.1) |
| 2025-02-24 10:51:29 +0100 | alfiee | (~alfiee@user/alfiee) (Ping timeout: 260 seconds) |