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Tagged with cartesian-closed-categories monoidal-categories
7
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Cartesian monoidal star-autonomous categories
Disclaimer: This is a crosspost (see MathStackexchange). Apologies if cross-posting is frowned upon. However, it seems that on Stackexchange there are not many people familiar with star-autonomous ...
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Strictifying closed monoidal categories?
Let C be a cartesian closed category. It's well known that C is equivalent to a category where the product is strict monoidal; i.e. where there are equalities of the functors given by the ...
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Does Cantor Bernstein hold in a Closed Symmetric Monoidal Category?
In a closed symmetric monoidal category with [I,X]≅X for all X is it true that having monomorphisms m:A→B and m:B→A is enough to imply A≅B ?
I tried to ...
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Is there a construction capturing indexed families of adjunctions?
I'm sorry in advance if this question does not belong on this site. I am curious as to what is "really" going on when you have a family of functors indexed by elements in a base category, all of which ...
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What is the monoidal equivalent of a locally cartesian closed category?
If a closed monoidal category is the monoidal equivalent of a Cartesian closed category, is there an analogous equivalent for locally cartesian closed categories? Is there a standard terminology or ...
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4
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Example of a non-closed cocomplete symmetric monoidal category
Background
By a cocomplete symmetric monoidal category C I mean a symmetric monoidal category whose underlying category is cocomplete and such that −⊗X:C→C is cocontinuous for all $X ...
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Seems like Reader monad composed with a strong monad produces a monad, am I right?
Take a Cartesian (or monoidal) closed category; define Reader monad for a given object E as
X↦XE; and take a strong monad M (strong means preserves product or tensor product).
Now the ...
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