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Post AXUCoHWJ3Rg1nOsPqK by [email protected] |
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Post #AXUCo9MnMvJcVaMhuK by [email protected] |
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Enriched Categories and Type TheoryEnriched categories are often presented as a… |
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Post #AXUCoCOg6NbVuIGkl6 by [email protected] |
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If you are familiar with enriched categories, this definition may be a bit ????… |
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Post #AXUCoDABFlbMHcUgng by [email protected] |
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@totbwf This description looks like defining a category enriched in a cartesian… |
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Post #AXUCoDEQzx0KUoU5Qm by [email protected] |
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@maxsnew I think it's a bit more delicate than that (we don't require a… |
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Post #AXUCoDIKlS7iguJCVc by [email protected] |
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@totbwf Did I require a set of objects? In type theory these would be Type-valu… |
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Post #AXUCoDLWZafwqnnkTw by [email protected] |
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You can improve the situation somewhat by defining only applying the yoneda tri… |
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Post #AXUCoDMwUJoGvCSsgy by [email protected] |
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@maxsnew Ah, I was assuming Set-valued presheaves; too much HoTT brain |
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Post #AXUCoE7jgLExGKMFd2 by [email protected] |
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@maxsnew I'm still puzzling over the categorical semantics of the leftover … |
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Post #AXUCoGUqrMv2cbBjw8 by [email protected] |
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Enter leftover typing! Instead of using context splits, we can have our morphis… |
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Post #AXUCoHWJ3Rg1nOsPqK by [email protected] |
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Unfortunately, these type-theoretic methods aren't totally free, and we pay… |
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Post #AXUCoJB6tDuUwEyW5A by [email protected] |
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@totbwf @maxsnew We need vocabulary to 'signal' Type-valued presheaves … |
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Post #AXUCoMBvgdLeHeNiHA by [email protected] |
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@JacquesC2 @totbwf @maxsnew Type-valued presheaves are \infty-presheaves, and t… |
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Post #AXUCoMGtOBJmX2hg0m by [email protected] |
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@MartinEscardo @totbwf @maxsnew CS stacks or math / alg-geom stacks? |
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Post #AXUCoMKRB09ai2MVXM by [email protected] |
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@JacquesC2 @MartinEscardo @totbwf @maxsnew - math stacks. |
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Post #AXWF4fZ01AFXDszwtk by [email protected] |
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@JacquesC2 @MartinEscardo @totbwf @maxsnew A stack is a (weak) presheaf of grou… |
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Post #AXWF4fdbk1w5SB9d56 by [email protected] |
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@boarders @MartinEscardo @totbwf @maxsnew I have encountered stacks before, whi… |
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Post #AXWF4fhVVX3TeGyk9w by [email protected] |
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@JacquesC2 - sheaves are not at all like generalized Riemann surfaces. A sheaf… |
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Post #AXWHCl5lXxDiauJFOC by [email protected] |
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@johncarlosbaez The sheaf condition seems to say that things must agree on the … |
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Post #AXWHClANGouGpCSvZY by [email protected] |
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@JacquesC2 - It's true that charts on a Riemann surface obey a condition t… |
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Post #AXWHCwDGCQkd5Ktt68 by [email protected] |
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@johncarlosbaez Actually, I should have said "generalized manifold". … |
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Post #AXWLH6k7OIU2iaVsrA by [email protected] |
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@johncarlosbaez @JacquesC2 Different examples click to different people. I have… |
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Post #AXWbb2hbinU9FFrmRE by [email protected] |
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@johncarlosbaez @JacquesC2 So when teaching it is good to offer a lot of exampl… |
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Post #AXWbb2mZQLSHUeBkAq by [email protected] |
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@MartinEscardo @JacquesC2 - "So when teaching it is good to offer a lot of… |
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Post #AXWbb9E5Sx1zTj6ntg by [email protected] |
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@johncarlosbaez @JacquesC2 I mean, there is a reason why Sketches of an Elephan… |
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Post #AXWmS6n8FR8kohOQcq by [email protected] |
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@johncarlosbaez @JacquesC2 Sheaves are on the other hand an excellent way to st… |
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Post #AXdAoe1CxGKs5V10gC by [email protected] |
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@JacquesC2 @johncarlosbaez @MartinEscardo There’s a super accessible intro to… |
