#homotopy — Public Fediverse posts

Elmendorf's theorem is a pathway to many abilities some consider to be equivariant.

#EquivariantHomotopy #homotopy

Elmendorf's theorem is a pathway to many abilities some consider to be equivariant.

#EquivariantHomotopy #homotopy

Elmendorf's theorem is a pathway to many abilities some consider to be equivariant.

#EquivariantHomotopy #homotopy

Elmendorf's theorem is a pathway to many abilities some consider to be equivariant.

#EquivariantHomotopy #homotopy

Elmendorf's theorem is a pathway to many abilities some consider to be equivariant.

#EquivariantHomotopy #homotopy

Can you define a 'simplicial set of small simplicial sets' by defining Δⁿ → Simp to be the set of small simplicial sets over Δⁿ, i.e. A → Δⁿ?

Would we then have that the maps B → Simp were in correspondence with the simplicial sets over B, for all B?

#CategoryTheory #SimplicialSets #Homotopy

Can you define a 'simplicial set of small simplicial sets' by defining Δⁿ → Simp to be the set of small simplicial sets over Δⁿ, i.e. A → Δⁿ?

Would we then have that the maps B → Simp were in correspondence with the simplicial sets over B, for all B?

#CategoryTheory #SimplicialSets #Homotopy

Can you define a 'simplicial set of small simplicial sets' by defining Δⁿ → Simp to be the set of small simplicial sets over Δⁿ, i.e. A → Δⁿ?

Would we then have that the maps B → Simp were in correspondence with the simplicial sets over B, for all B?

#CategoryTheory #SimplicialSets #Homotopy

Can you define a 'simplicial set of small simplicial sets' by defining Δⁿ → Simp to be the set of small simplicial sets over Δⁿ, i.e. A → Δⁿ?

Would we then have that the maps B → Simp were in correspondence with the simplicial sets over B, for all B?

#CategoryTheory #SimplicialSets #Homotopy

Can you define a 'simplicial set of small simplicial sets' by defining Δⁿ → Simp to be the set of small simplicial sets over Δⁿ, i.e. A → Δⁿ?

Would we then have that the maps B → Simp were in correspondence with the simplicial sets over B, for all B?

#CategoryTheory #SimplicialSets #Homotopy

Chris Staecker does humorous videos about calculation machines, but he also does research on digital #homotopy! Wait, what's that?!

A rather simple example for a digital space is just a digital image. We'll also need a digital sphere, and that's going to be the vertices of an octahedron. We want to do homotopy stuff, so we'll look at maps from any image to such an octahedron.

We're all used to looking at images, and since it's also where the fun happens, we'll color all the vertices of the octahedron in different colors, and pull those back to the image. So we can see where any pixel position gets mapped to by looking at its color.

Homotopy is a subject of topology, and that involves stretching. It also involves continuitiy, or a notion of neighbourhood. Both of these must be transported to our digital space and sphere.

Well, two vertices on an octahedron are neighbours if they are connected by an edge, or, put differently, they are not neighbours if they are opposite of each other. Now, when should we consider pixels on an image to be neghbours? Chris proposes that pixels, drawn as little squares, are considered to be neighbours if they share a vertex. Or an edge, which means that they share two vertices. So, any pixel in the middle of an image has eight neighbours!

1/3

Chris Staecker does humorous videos about calculation machines, but he also does research on digital #homotopy! Wait, what's that?!

A rather simple example for a digital space is just a digital image. We'll also need a digital sphere, and that's going to be the vertices of an octahedron. We want to do homotopy stuff, so we'll look at maps from any image to such an octahedron.

We're all used to looking at images, and since it's also where the fun happens, we'll color all the vertices of the octahedron in different colors, and pull those back to the image. So we can see where any pixel position gets mapped to by looking at its color.

Homotopy is a subject of topology, and that involves stretching. It also involves continuitiy, or a notion of neighbourhood. Both of these must be transported to our digital space and sphere.

Well, two vertices on an octahedron are neighbours if they are connected by an edge, or, put differently, they are not neighbours if they are opposite of each other. Now, when should we consider pixels on an image to be neghbours? Chris proposes that pixels, drawn as little squares, are considered to be neighbours if they share a vertex. Or an edge, which means that they share two vertices. So, any pixel in the middle of an image has eight neighbours!

1/3

Chris Staecker does humorous videos about calculation machines, but he also does research on digital #homotopy! Wait, what's that?!

A rather simple example for a digital space is just a digital image. We'll also need a digital sphere, and that's going to be the vertices of an octahedron. We want to do homotopy stuff, so we'll look at maps from any image to such an octahedron.

We're all used to looking at images, and since it's also where the fun happens, we'll color all the vertices of the octahedron in different colors, and pull those back to the image. So we can see where any pixel position gets mapped to by looking at its color.

Homotopy is a subject of topology, and that involves stretching. It also involves continuitiy, or a notion of neighbourhood. Both of these must be transported to our digital space and sphere.

Well, two vertices on an octahedron are neighbours if they are connected by an edge, or, put differently, they are not neighbours if they are opposite of each other. Now, when should we consider pixels on an image to be neghbours? Chris proposes that pixels, drawn as little squares, are considered to be neighbours if they share a vertex. Or an edge, which means that they share two vertices. So, any pixel in the middle of an image has eight neighbours!

1/3

Chris Staecker does humorous videos about calculation machines, but he also does research on digital #homotopy! Wait, what's that?!

A rather simple example for a digital space is just a digital image. We'll also need a digital sphere, and that's going to be the vertices of an octahedron. We want to do homotopy stuff, so we'll look at maps from any image to such an octahedron.

We're all used to looking at images, and since it's also where the fun happens, we'll color all the vertices of the octahedron in different colors, and pull those back to the image. So we can see where any pixel position gets mapped to by looking at its color.

Homotopy is a subject of topology, and that involves stretching. It also involves continuitiy, or a notion of neighbourhood. Both of these must be transported to our digital space and sphere.

Well, two vertices on an octahedron are neighbours if they are connected by an edge, or, put differently, they are not neighbours if they are opposite of each other. Now, when should we consider pixels on an image to be neghbours? Chris proposes that pixels, drawn as little squares, are considered to be neighbours if they share a vertex. Or an edge, which means that they share two vertices. So, any pixel in the middle of an image has eight neighbours!

1/3

I have neglected this channel, sorry lol. If you follow me you will probably find this interesting: https://arxiv.org/abs/2307.00442

#categories #homotopy #motives #gaugetheory #QFT

I have neglected this channel, sorry lol. If you follow me you will probably find this interesting: https://arxiv.org/abs/2307.00442

#categories #homotopy #motives #gaugetheory #QFT

I have neglected this channel, sorry lol. If you follow me you will probably find this interesting: https://arxiv.org/abs/2307.00442

#categories #homotopy #motives #gaugetheory #QFT

I have neglected this channel, sorry lol. If you follow me you will probably find this interesting: https://arxiv.org/abs/2307.00442

#categories #homotopy #motives #gaugetheory #QFT

Today I got to have the full #intuitionist #constructivist #maths experience.

First, somebody half-jokes that if one is a constructivist, then one's friends won't talk to them anymore.

Then, somebody else says that #constructivism is a deviant counterculture.

At this point, like a fool, I link Bauer's "five stages" paper: https://www.ams.org/journals/bull/2017-54-03/S0273-0979-2016-01556-4/S0273-0979-2016-01556-4.pdf

But alas, somebody actually reads the paper, and they think that the whole paper is a joke. They have two concrete questions, which I answer using relevant examples.

This was all in the context of #homotopy #TypeTheory, for what it's worth.

Today I got to have the full #intuitionist #constructivist #maths experience.

First, somebody half-jokes that if one is a constructivist, then one's friends won't talk to them anymore.

Then, somebody else says that #constructivism is a deviant counterculture.

At this point, like a fool, I link Bauer's "five stages" paper: https://www.ams.org/journals/bull/2017-54-03/S0273-0979-2016-01556-4/S0273-0979-2016-01556-4.pdf

But alas, somebody actually reads the paper, and they think that the whole paper is a joke. They have two concrete questions, which I answer using relevant examples.

This was all in the context of #homotopy #TypeTheory, for what it's worth.

Today I got to have the full #intuitionist #constructivist #maths experience.

First, somebody half-jokes that if one is a constructivist, then one's friends won't talk to them anymore.

Then, somebody else says that #constructivism is a deviant counterculture.

At this point, like a fool, I link Bauer's "five stages" paper: https://www.ams.org/journals/bull/2017-54-03/S0273-0979-2016-01556-4/S0273-0979-2016-01556-4.pdf

But alas, somebody actually reads the paper, and they think that the whole paper is a joke. They have two concrete questions, which I answer using relevant examples.

This was all in the context of #homotopy #TypeTheory, for what it's worth.

On this week's #blog , a bit late as I work around the start of teaching this semester, I write about the fascinating PhD thesis, 'On the homotopy groups of spheres in homotopy type theory' https://updatedscholar.blogspot.com/2023/02/discussing-on-homotopy-groups-of.html #Hott #TypeTheory #Homotopy

On this week's #blog , a bit late as I work around the start of teaching this semester, I write about the fascinating PhD thesis, 'On the homotopy groups of spheres in homotopy type theory' https://updatedscholar.blogspot.com/2023/02/discussing-on-homotopy-groups-of.html #Hott #TypeTheory #Homotopy

On this week's #blog , a bit late as I work around the start of teaching this semester, I write about the fascinating PhD thesis, 'On the homotopy groups of spheres in homotopy type theory' https://updatedscholar.blogspot.com/2023/02/discussing-on-homotopy-groups-of.html #Hott #TypeTheory #Homotopy

On this week's #blog , a bit late as I work around the start of teaching this semester, I write about the fascinating PhD thesis, 'On the homotopy groups of spheres in homotopy type theory' https://updatedscholar.blogspot.com/2023/02/discussing-on-homotopy-groups-of.html #Hott #TypeTheory #Homotopy

On this week's #blog , a bit late as I work around the start of teaching this semester, I write about the fascinating PhD thesis, 'On the homotopy groups of spheres in homotopy type theory' https://updatedscholar.blogspot.com/2023/02/discussing-on-homotopy-groups-of.html #Hott #TypeTheory #Homotopy

@buchholtz It's worth putting #HashTags in your posts to help people find relevant conversations:

#homotopy #TypeTheory

Give it time, but people will find each other.

And welcome!

@buchholtz It's worth putting #HashTags in your posts to help people find relevant conversations:

#homotopy #TypeTheory

Give it time, but people will find each other.

And welcome!

@buchholtz It's worth putting #HashTags in your posts to help people find relevant conversations:

#homotopy #TypeTheory

Give it time, but people will find each other.

And welcome!

@buchholtz It's worth putting #HashTags in your posts to help people find relevant conversations:

#homotopy #TypeTheory

Give it time, but people will find each other.

And welcome!

@buchholtz It's worth putting #HashTags in your posts to help people find relevant conversations:

#homotopy #TypeTheory

Give it time, but people will find each other.

And welcome!

#arbitrage #pricing #theory #decision #praxis #holonomy #information #manifold #curvature #noncommutative #geometry #modal #homotopy #type

#arbitrage #pricing #theory #decision #praxis #holonomy #information #manifold #curvature #noncommutative #geometry #modal #homotopy #type

imagine a #modal #homotopy #type #theory based on those modalities: #knowledge, #belief, and #perception

imagine a #modal #homotopy #type #theory based on those modalities: #knowledge, #belief, and #perception

#Introduction

Hello folks! I'm an undergraduate student in mathematics interested in abstract homotopy theory, and category theory at large! Aside from that, in my spare time I love programming, reading books and listening some good music!

I'm also into vegetarianism, philosophy, open source, looking forward to learn more about socialism and a variety of other topics :)

#maths #categoryTheory #homotopy #programming #music #books #openSource #philosophy #vegetarian #socialism

#Introduction

Hello folks! I'm an undergraduate student in mathematics interested in abstract homotopy theory, and category theory at large! Aside from that, in my spare time I love programming, reading books and listening some good music!

I'm also into vegetarianism, philosophy, open source, looking forward to learn more about socialism and a variety of other topics :)

#maths #categoryTheory #homotopy #programming #music #books #openSource #philosophy #vegetarian #socialism

#Introduction

Hello folks! I'm an undergraduate student in mathematics interested in abstract homotopy theory, and category theory at large! Aside from that, in my spare time I love programming, reading books and listening some good music!

I'm also into vegetarianism, philosophy, open source, looking forward to learn more about socialism and a variety of other topics :)

#maths #categoryTheory #homotopy #programming #music #books #openSource #philosophy #vegetarian #socialism

#Introduction

Hello folks! I'm an undergraduate student in mathematics interested in abstract homotopy theory, and category theory at large! Aside from that, in my spare time I love programming, reading books and listening some good music!

I'm also into vegetarianism, philosophy, open source, looking forward to learn more about socialism and a variety of other topics :)

#maths #categoryTheory #homotopy #programming #music #books #openSource #philosophy #vegetarian #socialism

very nice straight skeleton #addon for #b3d, and its free :)
https://github.com/Lichtso/straight_skeleton
#3d #2d #topology #homotopy #equivalence #math #geometry

very nice straight skeleton #addon for #b3d, and its free :)
https://github.com/Lichtso/straight_skeleton
#3d #2d #topology #homotopy #equivalence #math #geometry