The return of the retreating sun, which retrieves us from the dark of night, the pitch of winter, is a microcosmic recreation of the origination of the universe, the first birth of the sun.ĭonna Henes: Winter Solstice: Anniversary Celebration of Creation Stacey Nemour: Join Eckhart Tolle, Jim Carrey and John Raatz in Raising Consciousness Through Entertainment, Media and the Arts
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Whatever is happening on a microcosmic level is also happening in the larger reality it is all mirrored back. More specifically, she wants people to think about their relationship with crows as a kind of microcosmic example of their relationship with the natural world. I’ll try to get you to see that a lax monoidal functor F : 1 → D F : 1 \to D from the terminal monoidal category 1 1 to a monoidal category D D is the same as a monoid object in D D.The salts of the urine, called microcosmic salt, are often mistaken for gravel, but are distinguishable both by their angles of crystallization, their adhesion to the sides or bottom of the pot, and by their not being formed till the urine cools. So, let’s see how this fact is ‘explained’ in terms of lax maps. The monoid object (the ‘microcosm’) can only thrive in a category (a ‘macrocosm’) that resembles itself.
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We can define a monoid object inside any monoidal category - but a monoidal category is like a categorified monoid! So, for a monoid object to make sense in some category, that category needs to be like a categorified monoid object. Here’s the classic example of the microcosm principle. Let me try to explain this, because it’s really not as terrifying as it sounds. When Jim and I gave an n n-categorical formulation of the microcosm principle in terms of n n-categorical algebras of an operad O O, the key idea was to use lax maps from the terminal n n-categorical O O-algebra to a fixed n n-categorical O O-algebra. I’m glad more people are trying to find setups where the microcosm principle becomes a theorem - and thanks for pointing this out, David. And now you get the evident notion of rig object in a category with finite products to which you alluded (as well as all the less interesting examples which you enumerated). With δ \delta sending ( a, b, c ) ∈ A × ( B × C ) (a,b,c)\in A\times (B\times C) to ( a, b, a, c ) ∈ ( A × B ) × ( A × C ) (a,b,a,c)\in(A\times B)\times(A\times C). On the other hand, in the slides and associated paper, Hasuo, Jacobs and Sokolova give the principle a 2-categorical formulation as a lax natural transformation X : 1 ⇒ ℂ X: \mathbf is a category with finite products, then it has one of these “lax rig-category” structures with ⊗ \otimes
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Later, in section 4.3, they give a formal treatment of the principle using operads. the human soul) corresponds to some feature of the macrocosm. We name this principle the microcosm principle, after the theory, common in pre-modern correlative cosmologies, that every feature of the microcosm (e.g.
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11), as with monoid objects in a monoidal category. Recall their claim in Higher-Dimensional Algebra III that “certain algebraic structures can be defined in any category equipped with a categorified version of the same structure” (p. Furthering my study of coalgebra, I came across slides for a couple of talks ( here and here) which put John and Jim’s microcosm principle into a coalgebraic context.