estuary..fragmentation – gallery of anonymous sentimentality
#Experimental #ambient #apophenia #compositememorymap #decomposition #deconstructed #disorientation #dissociation #feildrecordings #hypermaximalist #hypersurreal #hypnogogia #lofiheartmusic #morphism #noise #sounddesign #Denver
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https://estuaryfragmentation.bandcamp.com/album/gallery-of-anonymous-sentimentality

UI UX Design Trends | Medium https://medium.com/@morshedurrana/ui-design-trends-in-2024-37cd3e1e51b0 #ui #trends #uitrends #Morphism

@sliverdaemon @tmbotg It's beyond myself, too, but I have an idea.

If the #inclusion #relation (a -> b iif a contained in b) is a #morphism of the Set category, its initial object would be the empty set, and "everything" would be the terminal object.

Although, for that to work, I think that the sets should be restricted to "proper" ones, to avoid Russell's #paradox: no sets containing themselves, which would means loops within the supposed lattice. So, a subcategory of the Set category.

#Morphism in category of small categories are functors

- { g:(X* Y)-> Z}, that is, { g\in [(X* Y)-> Z]}
[A->B]} :space of f: A-> B. By #currying, { {{curry}}(g):X-> [Y->Z]}
Apply -> #morphism
{{Apply}}:([Y-> Z]* Y)->Z},
so
{ {{Apply}}(f,y)=f(y)}
Ie commuting diagram

{ {Apply}}\circ \left({{curry}}(g)\times {{id}}_{Y}\right)=g}

- Every pos can be viewed as a #category in a natural way: there is a unique #morphism from x to y if and only if x ≤ y. A monotone #Galois connection is then nothing but a pair of adjoint #functors between two categories that arise from partially ordered sets.

a #morphism between smooth varieties is #étale at a point iff the differential between the corresponding tangent spaces is an #isomorphism. This is in turn precisely the condition needed to ensure that a map between manifolds is a local #diffeomorphism

a #morphism between smooth varieties is #étale at a point iff the differential between the corresponding tangent spaces is an #isomorphism. This is in turn precisely the condition needed to ensure that a map between manifolds is a local #diffeomorphism

An exact sequence is a sequence, either finite or infinite, of objects and morphisms between them such that the image of one #morphism equals the kernel of the next

An exact sequence is a sequence, either finite or infinite, of objects and morphisms between them such that the image of one #morphism equals the kernel of the next