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$G(S):= \lbrace y\in Y | \forall x\in S. xRy \rbrace$ $F(T):= \lbrace x\in X | \forall y\in T. xRy \rbrace$ This Galois connection is called “polarities” in “M. Erne, J. Koslowski, A. Melton, G. E. …

Is there a name for $(U,\eta)$ such that $(\eta, \eta^{op}):U^{op}\dashv U$ (is an adjunction). To clarify — $C:category$, $(I,I^{op})$ is the contravariant isomorphism with $I:C^{op}\to C$, $U:C^{op} …

In “Arbib, Manes. Arrows, Structures and Functors. The Categorical Imperative. 6. Structured sets.” there is an approach to formalize structures. I have a strong feeling that they describe just concre …

This is a reverse of the question “Is there a finitely complete category with terminal object but NO subobject classifier?” From “An informal introduction to topos theory” by Tom Leinster I learned th …

IMHO the answer to “where polynomials are initial” (not to the title question, which is too broad for me) is already given in “Awodey. Category theory. 9. Adjoints. 9.3. Examples of adjoints. Example …

I am trying to move in categorical algebra beyond the basics. A Lawvere theory L is a small category with finite products. (I know that there also is a functor $(skeleton(FinSet))^{op}\to L$, which re …