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| 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) |
| 2025-02-24 10:50:21 +0100 | merijn | (~merijn@77.242.116.146) (Ping timeout: 276 seconds) |
| 2025-02-24 10:48:33 +0100 | harveypwca | (~harveypwc@2601:246:d080:f6e0:34b5:bbb2:c6c:1ef6) (Quit: Leaving) |
| 2025-02-24 10:46:46 +0100 | alfiee | (~alfiee@user/alfiee) alfiee |
| 2025-02-24 10:46:27 +0100 | zmt00 | (~zmt00@user/zmt00) (Ping timeout: 276 seconds) |
| 2025-02-24 10:42:40 +0100 | zmt01 | (~zmt00@user/zmt00) zmt00 |
| 2025-02-24 10:42:11 +0100 | <Athas> | I suppose. I really don't want to be in the business of building abstractions, however. |
| 2025-02-24 10:41:25 +0100 | <tomsmeding> | you could always roll your own 2-dimensional array with manual divMod indexing |
| 2025-02-24 10:41:01 +0100 | <tomsmeding> | ah, that's how you got into this. :) |
| 2025-02-24 10:40:39 +0100 | <Athas> | I may just end up with vectors-of-vectors, even though it's not very efficient. |